Study Program Name Bachelor, Mathematics Department, … · Statement dalam pemrograman - QUIZ •...

Study Program Name Bachelor, Mathematics Department, FMKSD-ITS Course Name Algorithm and Programming Course Code KM184202 Semester 2 Sks 4

Supporting Lecturer Dr. Dwi Ratna Sulistyaningrum, MT, Alvida Mustika Rukmi, S.Si, M.Si

Materials

• Algorithm • Structured Programming • Recursive • GUI and Event Driven

Learning Outcome

[C2] Able to explain basic concepts of mathematics that includes the concept of a proof construction both logically and analytically, modeling and solving the simple problems, as well as the basic of computing.

[C3] Able to solve problems based on theoretical concepts in at least one field of mathematics: analysis and algebra, modeling and system optimization, and computing science.

COURSE LEARNING OUTCOME

1. Be able to understand the basic concepts of algorithms and procedural computer programming. 2. Be able to design algorithms, flow charts, and create computer programs with JAVA language

programming to solve mathematical problems, individually or togetherly.

Meets Sub Course Learning Outcome

Breadth of Materials Learning Methods Time Estimation

Student Learning

Experiences

Assessment Criteria and

Indicator

Weighting Assessment

(%) (1,2) Students are able to explain

the programming paradigm as well as to know the programming languages.

Understanding: o Definition of programming o Programming paradigm o Types of programming languages

Lecture Discussion

2x(2x50”)

Discussion

Accuracy describes the definitions and paradigms of programming and explains the programming language

(3,4) Students are able to explain the definition of the algorithm and know the algorithm criteria and able to make the program flowchart (2,3)

Definition of algorithm definition Explanation of algorithm criteria Explanation creates a program flowchart

Lecture Group Discussion

2x(2x50”) Task- (Problem & Solving)

Accuracy describes the definition of the algorithm and knows the algorithm criteria Precision create flowchart program

(5,6) Students are able to explain the definition of pseudo-code based on program flowchart (4)

Definition and manufacture of pseudocode

Lecture Discussion

2x(2x50”) Quiz-1 Precise create pseudocode based on flowchart

(7,8) Students are able to explain the basic principles of Java programming include data types, keywords, constants, variables

The concept of programming - Data type, keyword - Definitions of variables, constants - variables in programming - type and casting conversion - Scope the appropriate variables

Lecture Discussion

2x(2x50”)

• TaSks • Practice

• Accurate explanation of data types, keywords, variables, constants in Java • Accuracy of type and casting conversion • Actualization of exemplary examples.

(9,10) Students are able to apply the concept of Input-Output and Operator structure in programming.

I / O operation on java Operator assignment, bitwise on java Parentheses operator presedence on java

- Lecture - Discussion - Practice - Assignment

2x(2x50”) - TaSks - Discussion - Practice

Accuracy of using I / O Operation on java Operator assignment, bitwise on java Parentheses • operator presedence on java

(11,12, 13,14) Students are able to apply the concept of control structure (condition / branching and repetition) in programming.

‐ If Statement , Switch Statement , Break, Exit, dan Continue dalam pemrograman Java



• Accurate use of If Statement, Switch Statement, Break, Exit, and Continue in Java programming

‐ For Loop Statement, While Loop Statement, Do While Statement dalam pemrograman

- QUIZ • For Loop Statement, While Loop Statement, Do While Statement in programming • Presentation of taSks • Encoding skills

(15,16) MIDTERM EXAM (17,18,19) Students are able to apply the

concept of function (method) in programming.

Non argument function Parameters function


3x(2x50”) ‐ Task ‐ Practice

• Accuracy makes functions both non arguments and arguments • Mastering passing techniques

(20,21) Students are able to apply the concept of data type 1D and 2D arrays in programming.

Use of 1D and 2D array data types in programming



• Accuracy • Use of 1D and 2D array data types in programming • Encryption writing skills with the use of 1D and 2D array data types. • Accurate use of Data Type string • Creation of functions that perform simple search and slimming processes

(22,23) Students are able to apply recursive concept and compare with iterative

Students are able to develop a recursive method for mathematical functions

The recursive concept includes:

Understanding Recursive method for

mathematical functions [1]: Chapter 18 [2]: Chapter 20



Appropriateness explains the recursive concept

Clarity develops a recursive method for mathematical functions

Students are able to solve problems with recursive

(24,25,26) Students are able to apply string manipulation with String class library in JAVA

Use of String class library and method -


3x(2x50”) ‐ Task ‐ Practice ‐ QUIZ

The accuracy of using methods in the Java Class Library String for encoding requires string manipulation

(27,28) Students are able to apply Java GUI toolkit concept for GUI based programming

The use of components in the Java GUI toolkit includes: AWT, SWT, and Swing [1]: Chapter 14 Page 550 - 574 [2]: Chapter 12 p. 446 – 474



The precision of making Java GUI programming

(29,30) Students are able to understand Event-Driven concepts and are able to implement in Matlab

Event-Driven [1]: Chapter 14 Page 561 - 574 [2]: Chapter 16 Page 600 - 603



Accuracy of using event driven

Seriousness in working.

Create a simple program that involves event-driven

(31,32) FINAL EXAM

Reference Main : 1. Java Programming Comprehensive, 10th edition, Pearson Education, Inc., publishing as Prentice Pagel, 2013 2. Paul Deitel, Harvey Deitel, Java: How to Program, 9th edition, Prentice Pagel, 2012

Supporting :

1. Abdul Kadir, “Algoritma & Pemrograman Menggunakan Java”, Andi Offset, 2012

EVALUATIONANDASSESSMENTPLAN

Course : Algorithms And Programming, Code: KM184202, credits: 4 , semester:2

Mee

ting

Specific Learning Objective

(Sub‐Competency)

Elements of Competency in Assessment Number of

Questions

Form of Assessment

% Cognitive Psychomotor Affective

C1 C2 C3 C4 C5 C6 C7 P1 P2 P3 P4 P5 A1 A2 A3 A4 A5

(1,2) Students able to explain the paradigm of programming and know some programming languages.

√ √ √ Discussions

(3,4) Students able to explain the definition of algorithms and know the criteria of algorithm and able to construct a program flowchart

√ √ √ 4 Assignment- Problem & Solving)

10%

(5,6) Students able to explain the definition of pseudo code according to program flowchart

√ √ √ 3 Assignment 7.5%

(7,8) Students able to explain the basic principles of Java programming, including data types, keywords, constants, variables

√ √ √ 2 ‐ Assignment ‐ Practice

5%

(9,10, Students able to apply the concept of input-output structure and operator in programming.

√ √ √ 6 ‐ Assignment ‐ Discussions ‐ Practice

15%

11)) ‐ QUIZ 1

(12, 13,14)

Students able to apply the concept of control structure (condition/branching and looping) in programming.

√ √ √ 3 ‐ Assignment ‐ Discussions ‐ Practice ‐

7.5%

15,16

ETS

(17,18,19)

Students able to explain the concepts of function (method) in programming.


10%

(20,21) Students able to apply the concept of 1-D and 2-D array in programming.


10%

(22,23) Students able to apply the concept of recursive and compare it with iterative concept

Students able to develop recursive method for mathematical functions

Students able to solve problem using recursive approaches


7.5%

(24,25,26,)

Students able to apply string manipulation using class library String in JAVA

√ √ √ 6 ‐ Assignment ‐ Practice ‐ QUIZ 2

15%

(27, 28)Students able to apply the concept of GUI toolkit in Java to create a program based on GUI


7.5%

(29,30) Students able to understand the event-driven concept and able to implement it


5%

31, 32

EAS

Number Questions 40

Percentage 100%

Description :

C1 : Knowledge P1 : Imitation A1 : Receiving

C2 : Comprehension P2 : Manipulation A2 : Responding

C3 : Application P3 : Precision A3 : Valuing

C4 : Analysis P4 : Articulation A4 : Organization

C5 : Syntesis & Evaluation P5 : Naturalisation A5 : Characterization

C6 : Creative

Scoring Criteria

1. Assignment (10%)

After each chapter, there will be some exercises

2. Practice (20%)

Practice is conducted 8 times

3. Quiz I (10%)

Quiz I is conducted in the 6th week, to test the material from the beginning until 5th week with 4 questions of the same weight

4. Mid‐term exam (25%)

Mid‐term exam is conducted in 8th week, to test the material from the beginning until 7th week

5. Quiz II (10%)

Quiz II is conducted on 11th week, to test the material after the mid‐term exam until 12th week with 4 questions of the same weight

6. Final exam (25%)

Final exam is conducted in 16th week, to test the material from after the mid‐term exam until 15th week

AssessmentDesign

Week number‐ : 4 Assignment : 2

1. Assignment Objective : Students able to understand algorithm and able to construct algorithm from a real problem to a program flowchart (2,3)

2. Assignment Description a. Objects studied :

Creating flowchart from a real problem.

b. What needs to be done and its constraints : Creating a flowchart according to the given problem

c. Method to complete the assignment : The assignment is written on a paper

d. Outcome : Understand the method to create flowchart

3. Question example: A university offers credits for its courses with the following criteria:

Theory : one credit for 25 hours

Laboratories : one credit for 10 hours Create a flowchart that reads the number of hours in theory and the number of hours in laboratory that is taken by a student then compute the total credits

4. Scoring criteria

No. Aspect / Assessed Concept Score

1 Able to define the initial conditions and final conditions of the

algorithm :

Input : Number of theoretical hours and number of laboratory hours

Output : Total Credits

20

2 Able to draw the input and output processes 20

3 Able to draw the computation process 20

3 Able to create the complete flowchart completely and

correctly

40

Study Program Name Bachelor, Mathematics Department, FMKSD-ITS Course Name Algorithm and Programming Course Code KM184202 Semester 2 Sks 4

Supporting Lecturer Dr. Dwi Ratna Sulistyaningrum, MT, Alvida Mustika Rukmi, S.Si, M.Si

Materials

• Algorithm • Structured Programming • Recursive • GUI and Event Driven

Learning Outcome




1. Be able to understand the basic concepts of algorithms and procedural computer programming. 2. Be able to design algorithms, flow charts, and create computer programs with JAVA language

programming to solve mathematical problems, individually or togetherly.



Student Learning

Experiences

Assessment Criteria and

Indicator


(%) (1,2) Students are able to

explain the programming paradigm as well as to know the programming languages.

Understanding: o Definition of programming o Programming paradigm o Types of programming languages

Lecture Discussion

2x(2x50”)

Discussion

Accuracy describes the definitions and paradigms of programming and explains the programming language

(3,4) Students are able to explain the definition of the algorithm and know the algorithm criteria and able to make the program flowchart (2,3)

Definition of algorithm definition Explanation of algorithm criteria Explanation creates a program flowchart

Lecture Group Discussion

2x(2x50”) Task- (Problem & Solving)

Accuracy describes the definition of the algorithm and knows the algorithm criteria Precision create flowchart program

(5,6) Students are able to explain the definition of pseudo-code based on program flowchart (4)

Definition and manufacture of pseudocode

Lecture Discussion

2x(2x50”) Quiz-1 Precise create pseudocode based on flowchart

(7,8) Students are able to explain the basic principles of Java programming include data types, keywords, constants, variables

The concept of programming - Data type, keyword - Definitions of variables, constants - variables in programming - type and casting conversion - Scope the appropriate variables

Lecture Discussion

2x(2x50”)

• TaSks • Practice

• Accurate explanation of data types, keywords, variables, constants in Java • Accuracy of type and casting conversion • Actualization of exemplary examples.

(9,10) Students are able to apply the concept of Input-Output and Operator structure in programming.

I / O operation on java Operator assignment, bitwise on java Parentheses operator presedence on java



Accuracy of using I / O Operation on java Operator assignment, bitwise on java Parentheses • operator presedence on java

(11,12, 13,14) Students are able to apply the concept of control structure (condition /

‐ If Statement , Switch Statement , Break, Exit,

- Lecture - Discussion - Practice

4x(2x50”) - TaSks • Accurate use of If Statement, Switch Statement, Break,

branching and repetition) in programming.

dan Continue dalam pemrograman Java

‐ For Loop Statement, While Loop Statement, Do While Statement dalam pemrograman

- Assignment - Discussion- Practice - QUIZ

Exit, and Continue in Java programming • For Loop Statement, While Loop Statement, Do While Statement in programming • Presentation of taSks • Encoding skills

(15,16) MIDTERM EXAM (17,18,19) Students are able to apply

the concept of function (method) in programming.

Non argument function Parameters function



• Accuracy makes functions both non arguments and arguments • Mastering passing techniques

(20,21) Students are able to apply the concept of data type 1D and 2D arrays in programming.

Use of 1D and 2D array data types in programming



• Accuracy • Use of 1D and 2D array data types in programming • Encryption writing skills with the use of 1D and 2D array data types. • Accurate use of Data Type string • Creation of functions that perform simple search and slimming processes

(22,23) Students are able to apply recursive concept and compare with iterative

Students are able to develop a recursive method for

The recursive concept includes:

Understanding Recursive method for

mathematical functions [1]: Chapter 18 [2]: Chapter 20



Appropriateness explains the recursive concept

Clarity develops a recursive

mathematical functions

Students are able to solve problems with recursive

method for mathematical functions

(24,25,26) Students are able to apply string manipulation with String class library in JAVA

Use of String class library and method -


3x(2x50”) ‐ Task ‐ Practice ‐ QUIZ

The accuracy of using methods in the Java Class Library String for encoding requires string manipulation

(27,28) Students are able to apply Java GUI toolkit concept for GUI based programming

The use of components in the Java GUI toolkit includes: AWT, SWT, and Swing [1]: Chapter 14 Page 550 - 574 [2]: Chapter 12 p. 446 – 474



The precision of making Java GUI programming

(29,30) Students are able to understand Event-Driven concepts and are able to implement in Matlab

Event-Driven [1]: Chapter 14 Page 561 - 574 [2]: Chapter 16 Page 600 - 603



Accuracy of using event driven

Seriousness in working.

Create a simple program that involves event-driven

(31,32) FINAL EXAM

Reference Main : 1. Java Programming Comprehensive, 10th edition, Pearson Education, Inc., publishing as Prentice Pagel,

2013 2. Paul Deitel, Harvey Deitel, Java: How to Program, 9th edition, Prentice Pagel, 2012

Supporting :


Course

Course Name : Algorithm and Programming

Course Code : KM184202

Credit : 4

Semester : 2

Description of Course

Algorithms and programming is course that discuss the basic concepts of algorithms and procedural programming. The concepts of algorithm and programming is implemented in JAVA programming language and will be used to solve simple problems. The topic include: basic algorithms, data types, variables, I/O structures, operators, loops, control structures, functions and procedures, array, string manipulation, recursive, GUI and event driven. The teaching system include tutorials, responses and scheduled workshops.

Learning Outcome

[C2]

Able to explain basic concepts of mathematics that includes the concept of a proof construction both logically and analytically, modeling and solving the simple problems, as well as the basic of computing.


Course Learning Outcome

1. Be able to understand the basic concepts of algorithms and procedural computer programming.

2. Be able to design algorithms, flow charts, and create computer programs with JAVA language programming to solve mathematical problems, individually or togetherly.

Main Subject

1. Algorithms: definition, criteria, flow chart, pseudo-code 2. Programming Concepts: paradigms, structured programming steps,

programming languages 3. Java Programming Language: data types, keywords, constants, variables,

I/O structures, operators, loops, control structures, functions and procedures, array, string manipulation, recursive, GUI and event driven.

Prerequisites

Reference

1. Java Programming Comprehensive, 10th edition, Pearson Education, Inc., publishing as Prentice Hall, 2013

2. Paul Deitel, Harvey Deitel, Java: How to Program, 9th edition, Prentice Hall, 2012

Supporting Reference


Study Program Name Bachelor, Mathematics Department,FMKSD-ITS Course Name Artificial Neural Networks Course Code KM184828 Semester 8 Credits 2 Supporting Lecturer Prof. Dr. Mohammad Isa irawan, MT

Materials

Modeling of ANN Matriks computation Algorithms in Artificial Neural Networks (ANNs) Some Aplications of ANNs

Learning Outcome

[C4]

Able to illustrate the framework of mathematical thinking in particular areas such as analysis, algebra, modeling, system optimization and computing science to solve real problems, mainly in the areas of environment, marine, energy and information technology.

[C5] Able to explain ideas and knowledge in mathematics and other fields to the society, in similar professional organizations or others.

[C5] Able to choose decisions and alternative solutions using data and information analysis based on an attitude of leadership, creativity and have high integrity in completing work individually or in a team.


1. Students are able to explain in any field the application of ANN 2. Students are able to analyze the simplest ANN algorithm to recognize AND, OR, NAND

and NOR logic patterns. 3. Students are able to well explain the different implementation of ANN algorithm with 1

processing element and multi processing element. 4. Students are able to properly explain the network capable of storing memory 5. Students are able to properly explain the basic concepts of competition-based networks and

problems that the network can solve 6. Students are able to explain the difference between the concept of backpropagation and

variation network algorithms 7. Students are able to properly examine the scientific work on the ANN application



Student Learning

Experiences

Assessment Criteria and Indicator

Weighting

Assessment (%)

(1) Students are able to explain where A neural network is applied.

‐ contracts Subject ‐ The introduction of artificial

neural network applications [1] Irawan Chapter I

Lecture Introduction, simple case studies, group discussions

1x (2x50 ") Writing about some of the problems given solutions

Good skills in explaining in any field of application of ANN

5 %

(1,2) Students are able to explain the neural network modeling of biological neural networks and artificial neural network algorithm simplest

‐ Fundamentals of computational models of neural networks 1 network processing elements

‐ Hebs algorithm, ‐ Perceptron, and ‐ There is line [1] Irawan Chapter I

- Lecture - Exercises


Being able to analyze the simplest neural network algorithm to recognize patterns of logical AND, OR, NAND and NOR

10%

(3) Students are able to implementation of simple artificial neural network algorithm to identify simple patterns

‐ Project presentation simple algorithm application Hebs., Perceptron and Adaline

[1] Irawan Chapter II

Practice

1x (2x50 ") ‐ Source code is the result of lab

‐ Writing about some of the problems given solutions

Good skills in explaining differences in neural network algorithm imple-tion 1 processing elements

The precision-kan become clear implementation

5 %

(4,5) Students are able to explain the concept and application of artificial neural network algorithm that is capable of storing a memory

‐ Assosiative Memory ‐ counter Propagation ‐

Lecture, Review session

2x (2x50 ") ‐ Writing about some of the problems given solutions

‐ Quis I

Skill in explaining the network is capable of storing a memory

10 %

(6) Students are able to explain the basic concept

‐ Kohonen SOM ‐ LVQ


1x (2x50 ") ‐ Writing about some of the

Skill in explaining the basic concepts of

10 %

of a neural network-based competition

problems given solutions

network-based competition

(7) Students are able to apply the concept of competition in the neural network through simple examples

‐ Presentation simple project SOM Kohonen network, LVQ and Counter Propagation for clustering and data classification

Practice



Appropriateness explained types based competition

Have an idea about solving problems with the help of a network-based competition

10%

8 MIDTERM EXAM (9) Students are able to

examine the papers on artificial neural network that utilizes the concept of competition

‐ Review of scientific work / paper application Kohonen SOM, LVQ and Counter Propagation

Group discussion,

1x (2x50 ") Concise writing the review of scientific work on SOM Kohonen network, LVQ and Counter propagation

Good skills in the review of scientific work on application Kohonen SOM, LVQ and Counterpropagation

Have an idea about solving problems with the help of Kohonen SOM, LVQ and Counterpropagation

10%

(10,11) Students are able to explain the concept and its variations backpropagation network

‐ Backpropagation network ‐ Variation

Lecture, Group discussion, 2x (3x50 ")]


Good skills in explaining different concepts backpropagation network algorithm and its variations

20 %

(12) Students are able to explain the concept of network applications and variations backpropagation

‐ Backpropagation network application for pattern recognition of data

‐ Backpropagation network applications for forecasting

Lecture, Group discussion,


Good skills in explaining the network application backpropagation for pattern recognition and forecasting

10%

(13) Students are able to explain the imple-tion nets backpropagation for pattern recognition

‐ Project presentation Backpropagation network applications and variations



Appropriateness explained the types of back propagation algorithm

10 %

Reference Main :

1. Irawan, M. Isa, “Dasar-Dasar Jaringan Syaraf Tiruan ”, ITS Press, 2013

Supporting :

1. Laurene Fauset, “Fundamental of Artificial Neural Networks”, Penerbit Prentice Hall, 1994 2. Simon Haykin, “Kalman Filtering and Neuralnetwork”, Penerbit John Wiley & Sons, 2001 3. James A. Freeman and David M. Skapura, “Neural Networks Algorithms, Applications, and Programming

Techniques”, Penerbit Addison Wesley, 1991


‐ Quiz II

Have an idea about solving problems with network support backprropagation

(14, 15) students are able to read scientific papers that apply neural networks to solve problems

‐ Assessing international journals or proceedings

Presentation

2x (2x50 ") ‐ Summary results of the study


The accuracy describes understanding and solving cases

20%

16 FINAL EXAM

STUDENTLEARNINGEVALUATIONPLAN

Course : Artificial Neural Networks, Code: KM184828, sks:2 sks, smt:8 Learning Outcome :

1. Able to illustrate the framework of mathematical thinking in particular areas such as analysis, algebra, modeling, system optimization and computing science to solve real problems, mainly in the areas of environment, marine, energy and information technology.

2. Able to explain ideas and knowledge in mathematics and other fields to the society, in similar professional organizations or others. 3. Able to choose decisions and alternative solutions using data and information analysis based on an attitude of leadership, creativity and

have high integrity in completing work individually or in a team.

Meets


(Sub‐Competence)

Elements of Competency in Assessment Questio

ns Number

Form of Assessment



1

Students are able to explain where A neural network is applied.

X

X

X X 3 ‐ Non-test ‐ Lecture note

5

2 Students are able to explain the neural network modeling of biological neural networks and artificial neural network algorithm simplest

X

X


5

3 Students are able to implementation of simple artificial neural network algorithm to identify simple patterns

X

X


5

4,5 Students are able to explain the concept and application of artificial neural network algorithm that is capable of storing a memory

X

X


15

6,7

Students are able to explain the basic concept of a neural network-based competition

X X

X


15

8 MIDTERM EXAM

9 Students are able to apply the concept of competition in the neural network through simple examples

X X


5

10,11 Students are able to examine the papers on artificial neural network that utilizes the concept of competition

X X X X X 2 ‐ Non-test ‐ Demo Program

10

12 Students are able to explain the concept and its variations backpropagation network

X X X X X 3 ‐ Non-test ‐ Lecture note

5

13 Students are able to explain the concept of network applications and variations backpropagation

X X X X 3 ‐ Non-test ‐ Lecture note

15

14 Students are able to explain the implantation nets backpropagation for pattern recognition

X X X X 3 ‐ Non-test ‐ Lecture note

10

15 students are able to read scientific papers that apply neural networks to solve problems

X X X X X X 2 ‐ Non-test ‐ Demo Program

15

16 FINAL EXAM

Meets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Number Questions item 3 3 3 3 3 3 3 ETS 3 2 2 3 3 3 2 EAS

Percentage 5 5 5 15 15 5 5 5 5 15 10 15 100%

Informations :






C6 : Creative

FormatofTaskDesignStudy Program Name Bachelor, Mathematics Department,FMKSD-ITS Course Name Artificial neural networks Course Code KM184828

Semester 8 Credits 2 Supporting Lecturer Prof. Dr. Mohammad Isa Irawan, MT

Weeks : 4, 5 Task : 1

1. Purpose of task : Students are able to demonstrate through a simple program in Java or MATLAB to implemented Perceptron algorithm to recognized operator logic AND, OR, NAND dan NOR.

2. Task description a. Claim object :

Project programming - Implementation of perceptron algorithm to recoqnized operator logic.

b. What to do and limitation : Create a program that can demonstrate ability of perceptron to memorize input-output data, and recoqnized the pattern

c. Description of output of work produced / done: Report and program that must be presented in front of other students

3. Assessment criteria

No. Assessed Aspects / Concepts Score

1 Able to demonstrate ability of perceptron algorithm 30

2 Able to implement in programming language Java / Python, minimum in MATLAB

40

3 Able to demonstrate the program well, user friendly, and beautiful 30

Score Total 100

FormatofTaskDesign

Study Program Name Bachelor, Mathematics Department,FMKSD-ITS

Course Name Artificial Neural Networks Course Code KM184828

Semester 8 Credits 2 Supporting Lecturer Prof. Dr. Mohammad Isa irawan, MT

Week - : 15 Task : 2

1. Purpose of task : Student able to explain others algorithms that have not implemented yet in a project.

2. Task description a. Claim object : Explain a part of book which contain an algorithm of ANNs b. What to do and limitation :

Make a presentation to explain an algorithm which has not implemented in project programming.

c. Method/way of done reference used: Tasks are typed in a power point that contain algorithm, and example of

application. d. Description of output of work produced / done:

A power point and translation in word.

3. Assessment criteria 4.


1 Able to explain one or more other algorithm which have not been implemented yet in the programming project

30

2 Able to explain using examples from literature 40

3 Able to explain clearly and systematically 30

Score total 100

Test Plan

Study Program Name Bachelor, Mathematics Department,FMKSD-ITS Course Name Artificial Neural Networks Course Code KM184828

Semester 8 Credits 2 Supporting Lecturer Prof. Dr. Mohammad Isa Irawan, MT

Example of description test

Course Name : Artificial neural networks Date : Friday, 01‐04‐2016 Duration/Type : 100 minutes / Closed Book Lecturer : Prof. Dr. M. Isa Irawan, MT

ATTENTION!!! Any kind of violation (cheating, working together, etc.) that are done during Midterm Test or Final Test will be sanctioned with courses cancellation in the current semester.

1. By using a bipolar input (X1, X2) and target t, compare the result if we use Hebb network

and Perceptron for training process of NOR function. How many iterations created? What

conclusions can be drawn? (Alpha = 1, threshold = 0.1)

2. By using a bipolar input (X1, X2) and target t, compare the result if we use Perceptron for

training process of AND NOT function. How many iterations created? What conclusions

can be drawn? (Alpha = 1, threshold = 0.1)

3. Adaline network is used to recognize pattern of 2 bipolar input and 1 bipolar output with

its target. Obtain the last weight from your Adaline network that can recognize NAND

logic pattern well. Use the activation function. Tolerate value is 0.5.

𝑦1, 𝑖𝑓 𝑦 01, 𝑖𝑓 𝑦 0

The algorithm of Adaline is:

Step 0: Weight initialization

(very small random value)

Set the learning rate 𝛼

Step 1: If the stopping condition is not fulfilled, do step 2‐6

Step 2: for every bipolar pair (s:t) do step 3‐5

Step 3: Set activation from input unit 𝑖 1,2,3, … , 𝑛:

𝑥 𝑠

Step 4: Calculate the input network towards output unit:

𝑦 𝑏 ∑ 𝑥 𝑤

Step 5: Update the bias and weight 𝑖 1,2,3, … , 𝑛:

𝑏 𝑛𝑒𝑤 𝑏 𝑜𝑙𝑑 𝛼 𝑡 𝑦

𝑤 𝑛𝑒𝑤 𝑤 𝑜𝑙𝑑 𝛼 𝑡 𝑦 𝑥

Step 6: Check the stopping condition, if the biggest weight in step 2 is

smaller than the tolerate value, then stop, otherwise continue

Diusulkan / Proposed Prof. Dr. M. Isa Irawan, MT Dosen Pengampu

Ditelaah / ReviewedProf. Dr. M. Isa Irawan, MT Ketua RMK Komputasi

Disetujui / Approved Dr. Didik Khusnul Arif, S.Si, M.Si Kaprodi Sarjana (S1) Matematika

Study Program Name Bachelor, Mathematics Department, FMKSD-ITS Course Name Artificial Neural Network Course Code KM184828 Semester 8 SKS 2 Supporting Lecturer Prof. Dr. Mohammad Isa Irawan, MT

Materials

Artificial Neural Network

Learning Outcome

[C4]



[C5]

Able to choose decisions and alternative solutions using data and information analysis based on an attitude of leadership, creativity and have high integrity in completing work individually or in a team.


1. Students are able to explain in any field the application of ANN 2. Students are able to analyze the simplest ANN algorithm to recognize AND, OR, NAND

and NOR logic patterns. 3. Students are able to well explain the different implementation of ANN algorithm with 1

processing element and multi processing element. 4. Students are able to properly explain the network capable of storing memory 5. Students are able to properly explain the basic concepts of competition-based networks

and problems that the network can solve 6. Students are able to explain the difference between the concept of backpropagation and

varietin network algorithms 7. Students are able to properly examine the scientific work on the ANN application


Breadth of Materials Learning methods Time Estimation

Student Learning

Experiences


Weighting

Assessment (%)

(1) Students are able to explain where A neural network is applied.

‐ contracts Subject ‐ The introduction of artificial

neural network applications [1] Irawan Chapter I

Lecture Introduction, simple case studies, group discussions


Good skills in explaining in any field of application of ANN

5%

(1,2) Students are able to explain the neural network modeling of biological neural networks and artificial neural network algorithm simplest

‐ Fundamentals of computational models of neural networks 1 network processing elements

‐ Hebs algorithm, ‐ Perceptron, and ‐ There is line [1] Irawan Chapter I

- Lecture - Exercises


Being able to analyze the simplest neural network algorithm to recognize patterns of logical AND, OR, NAND and NOR

10%

(3) Students are able to implementation of simple artificial neural network algorithm to identify simple patterns

‐ Project presentation simple algorithm application Hebs., Perceptron and Adaline

[1] Irawan Chapter II

Practice



Good skills in explaining differences in neural network algorithm imple-tion 1 processing elements

The precision-kan become clear implementation

5%

(4,5) Students are able to explain the concept and application of artificial neural network algorithm that is capable of storing a memory

‐ Assosiative Memory ‐ counter Propagation ‐



‐ Quis I

Skill in explaining the network is capable of storing a memory

10%

(6) Students are able to explain the basic concept of a neural network-based competition

‐ Kohonen SOM ‐ LVQ



Skill in explaining the basic concepts of network-based competition

10%

(7) Students are able to apply the concept of competition in the neural network through simple examples

‐ Presentation simple project SOM Kohonen network, LVQ and Counter Propagation for clustering and data classification

Practice



Appropriateness explained types based competition

Have an idea about solving problems with the help of a network-based competition

10%

8 MIDTERM EXAM (9) Students are able to

examine the papers on artificial neural network that utilizes the concept of competition

‐ Review of scientific work / paper application Kohonen SOM, LVQ and Counter Propagation

Group discussion,

1x (2x50 ") Concise writing the review of scientific work on SOM Kohonen network, LVQ and Counter propagation

Good skills in the review of scientific work on application Kohonen SOM, LVQ and Counterpropagation

Have an idea about solving problems with the help of Kohonen SOM, LVQ and Counterpropagation

10%

(10,11) Students are able to explain the concept and its variations backpropagation network

‐ Backpropagation network ‐ Variation

Lecture, Group discussion, 2x (3x50 ")]


Good skills in explaining different concepts backpropagation network algorithm and its variations

20%

(12) Students are able to explain the concept of network applications and variations backpropagation

‐ Backpropagation network application for pattern recognition of data

‐ Backpropagation network applications for forecasting



Good skills in explaining the network application backpropagation for pattern recognition and forecasting

10%

(13) Students are able to explain the imple-tion nets backpropagation for pattern recognition

‐ Project presentation Backpropagation network applications and variations




Appropriateness explained the types of back propagation algorithm

Have an idea about solving problems with

10%

Reference Main :

1. Irawan, M. Isa, “Dasar-Dasar Jaringan Syaraf Tiruan ”, ITS Press, 2013

Supporting :

1. Laurene Fauset, “Fundamental of Artificial Neural Networks”, Penerbit Prentice Pagel, 1994 2. Simon Haykin, “Kalman Filtering and Neuralnetwork”, Penerbit John Wiley & Sons, 2001 3. James A. Freeman and David M. Skapura, “Neural Networks Algorithms, Applications, and

Programming Techniques”, Penerbit Addison Wesley, 1991

‐ Quiz II network support backprropagation

(14, 15) students are able to read scientific papers that apply neural networks to solve problems

‐ Assessing international journals or proceedings

Presentation

2x (2x50 ") ‐ Summary results of the study


The accuracy describes understanding and solving cases

20%

16 FINAL EXAM

Course

Course Name : Artificial Neural Network


Credit : 2

Semester : 8


The course of artificial neural networks is a course that studies computational algorithms that mimic how biological neural networks work. This course is part of the Data Science, because the algorithm learned works well when applying data processing.

Learning Outcome

[C4]





1. Students are able to explain in any field the application of ANN 2. Students are able to analyze the simplest ANN algorithm to recognize

AND, OR, NAND and NOR logic patterns. 3. Students are able to well explain the different implementation of ANN

algorithm with 1 processing element and multi processing element. 4. Students are able to properly explain the network capable of storing

memory 5. Students are able to properly explain the basic concepts of competition-

based networks and problems that the network can solve 6. Students are able to explain the difference between the concept of

backpropagation and varietin network algorithms 7. Students are able to properly examine the scientific work on the ANN

application

Main Subject

1. Modeling of artificial neural networks from biological neural networks, 2. A simple pattern recognition with Perceptron, Hebb and Adaline, 3. Character recognition with Percepron, Associative memories, 4. Classification with BP, and LVQ, 5. Clustering with Kohonen SOM, 6. Forecasting BP, and RBF 7. Alternative model of ANN

Prerequisites

Linear Algebra Elementer Computer Programming

Reference

1. Irawan, M. Isa, “Dasar-Dasar Jaringan Syaraf Tiruan ”, Penerbit ITS Press, 2013


1. Laurene Fauset, “Fundamental of Artificial Neural Networks”, Penerbit Prentice Hall, 1994

2. James A. Freeman and David M. Skapura, “Neural Networks Algorithms, Applications, and Programming Techniques”, Penerbit Addison Wesley, 1991

3. Simon Haykin, “Kalman Filtering and Neuralnetwork”, Penerbit John Wiley & Sons, 2001

Study Program Name Bachelor, Mathematics Department, FMKSD-ITS

Course Name Elementary Linear Algebra

Course Code KM184203

Semester 2

Sks 4

Supporting Lecturer Dian Winda S, SSi, MSi

Materials

• Matrices and Vectors • Vector Space • Linear Transformation

Learning Outcome




1. Students are able to follow developments and apply mathematics and be able to communicate actively and correctly either oral or written.

2. Students are able to explain intelligently and creatively about the significant role of ALE applications in the field of related knowledge clusters and other fields.

3. Students have a special ability and able to process their ideas enough to support the next study in accordance with the related field.

4. Students are able to present their knowledge in Elementary Linear Algebra independently or in teamwork.


Breadth of Materials Learning Methods Time Estimatio

n

Student Learning

Experiences


Weighting

Assessment (%)

1-4

• Students are able to complete the SPL by the Gaussian or Gauss Jordan elimination method And able to explain why SPL has no settlement. • Students are able to use operations on the matrix and understand the algebraic properties of the matrix

• The understanding of system of linear equation and augmented matrix • Elementary Row Operation • Gaussian and Gauss Jordan elimination • Operation Matrix. the properties of algebra in the matrix [Ref. 1 page: 9-98]

• Lectures, • Student conditioning, • Question and answer. • Giving exercise • Group discussion,

4x(2x50’)

Task Exercise questions

• Accuracy defines system of linear equation and augmented matrix. • Ability to solve system of linear equation by elementary row operation • Be able to solve using Gaussian and Gauss Jordan • Be able to explain the properties of algebra in the matrix

15%

5-6 • Students are able to find inverse matrix, can complete system of linear equation by inversing matrix • Students recognize the types of matrices and properties of the matrix

• Looking for Inverse matrix • Complete the system of linear equation with the inverse matrix • Matrix type: Diagonal matrix, triangular matrix, symmetry matrix and its properties [Ref. 1 page: 99-139]

• Lectures, • Student conditioning, • Question and answer. • Giving exercise • Group discussion

2x(2x50’)

Task Exercise questions

• Be able to get the inverse of a matrix • Able to complete system of linear equation by inversing matrix • Be able to explain the types and properties of the matrix

5%

7-8 • Students are able to find the determinant of a matrix with Cofactor expansion • Students are able to find the determinant of a matrix by Row Reduction • Students are able to understand the properties of the determinant

• Counting determinants with Cofactor expansion • Counting determinants by Reducing Rows • the properties of the determinant • complete SPL with Cramer rules [Ref. 1 page: 173-211]


2x(2x50’) Task Exercise questions

• Able to calculate determinants with Cofactor expansion • Capable of Counting determinants by Row Reduction • Be able to explain the properties of the determinant

10%

• Students are able to complete the system of linear equation with the Cramer's rules

• Able to complete SPL with Cramer rules

9-12 Students are able to understand the vectors in space 2, space 3 and space n and operation on the vector

Students are able to define norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry from linear System

vector in space 2, space 3 and space n

operation on the vector norm, dot product, distance, cross product, orthogonal set at R ^ n, set geometry of linear system [Ref. 1 page: 226-320]


2x(2x50’) Task Exercise questions

Able to explain vectors in space 2, space 3 and space n

Be able to explain the operation on the vector

Ability to explain and norm, product of point (product dot), distance, cross product, orthogonal set at 𝑅 , seta geometry of linear System equation

15%

13,14 • Students are able to understand real vector spaces • Students are able to understand the real vector subspace • Students are able to understand linear and linearly independent combinations

• real vector space • real vector subspace • linear and linearly independent combinations [Ref. 1 page: 328-375]


2x(2x50’) TaSks Exercise questions

• Be able to explain real vector spaces and real vector subspaces • Be able to explain linear combinations and linearly independent sets

5%

15,16 Midterm Exam

17-19 • Students are able to understand the basis and dimension of a vector space • Students are able to determine the relative

• Base • The vector space dimension • Relative Coordinates • Transition Matrix • Classroom, Column Room, Empty Room


2x(2x50’) Tasks Exercise questions

• able to explain the basis and dimension of a vector space • able to determine the relative coordinates of

15%

coordinates of a vector on a basis in a vector space • Students are able to understand the row space, column space, blank space, rank, nullity of a matrix

• Rank and nullity [Ref. 1 page: 377-455]

a vector to a basis in a vector space • able to explain the row space, column space, empty space, rank, nullity of a matrix

20-22 Students are able to understand the transformation of matrices from 𝑅 to 𝑅

Students are able to understand composition in matrix transformation

Definition of matrix transformation from R ^ n to R ^ m and its types

How to get the Matrix Transformation

Composition on the transformation matrix

[Ref. 1 thing: 456-515]



The student is able to explain the matrix transformation from 𝑅 to 𝑅

Students are able to explain Composition on matrix transformation

10%

23-25 • Students are able to determine the eigenvalues and eigenvectors of a square matrix • Students are able to determine the requirements of the matrix to be diagonalizable and can diagonalize the matrix

Eigenvalues Eigenvector Diagonalization of matrix 𝐴

with invertible matrix 𝑃 so that 𝐷 𝑃 𝐴𝑃

[Ref. 1 page: 539-569]



• able to determine eigenvalues and eigenvectors of a square matrix • able to determine the requirement of the matrix to be diagonalizable and can diagonalize the matrix

10%

26-30 • Students are able to understand inner product results in real vector spaces • Students are able to understand the set of orthogonol in the inner product space • Students are able to form an orthonormal basis by performing the Gram-Schmidt process

• Understanding Inside Outcomes • the orthogonal set • Gram-Schmidt process [Ref. 1 page: 608-660]



• able to explain inner product in real vector space • Students are able to explain the set of orthogonol in the inner product space • able to form an orthonormal basis by performing the Gram-Schmidt process

15%

Reference Main :

1. Howard Anton and Chris Rorrers, ”Elementary Linear Algebra, Tenth Edition", John Wiley and Sons, (2010).

Supporting : 1. C.D. Meyer,”Matrix Analysis and Applied Linear Algebra”, SIAM, (2000) 2. Steven J. Leon, "Linear Algebra with Applications", Seventh Edition, Pearson Prentice Pagel, (2006). 3. Stephen Andrilli and David Hecker,”Elementary Linear Algebra, Fourth Edition”, Elsevier, (2010) 4. Subiono., ”Ajabar Linear”, Jurusan Matematika FMIPA-ITS, 2016.

31-32 FINAL EXAM


Courrse : Elementary Linear Algebra, Code: KM184203, sks: 4 sks, smt: 2

Learning Outcome:

1. Able to interpret basic mathematical concepts and compile evidence directly, indirectly, or with mathematical induction. 2. Able to identify simple problems, form mathematical models and solve them. 3. Mastering standard methods in the field of mathematics 4. Able to master the fundamental theory of mathematics which includes the concepts of set, function, differential, integral, space and mathematical structure. 5. Able to analyze the system and optimize its performance 6. Able to understand mathematical problems, analyze and solve them. 7. Able to observe, recognize, formulate and solve problems through mathematical approaches

Meets

Spesific Learning Objective

(Sub‐Competence)


questions

Form of Assessment



1-4

• Students are able to complete SPL with the Gaussian or Gauss Jordan elimination method As well as being able to explain why the SPL has no solution. • Students are able to use operations on the matrix and understand the properties of algebraic spheres on the matrix

√

√

3 Task Training Questions

15%

5-6 • Students are able to find matrix inverses, can solve SPL with matrix inverses Students recognize the types of matrices and the properties of the matrix

√

√ 1 Task Training Questions

5%

7-8 • Students are able to find the determinant of a matrix with Cofactor expansion • Students are able to find the determinant of a matrix with Line Reduction • Students are able to understand the properties of determinants • Students are able to complete SPL with the rules of cramer

√

√

√

√


10%

9-12 Students are able to understand vectors in space 2, space 3 and space n and operations in vectors Students are able to determine norms, point products (dot products), distances, cross times (cross products), orthogonal sets at R ^ n, after geometry of linear systems

√

√


15%

13,14 • Students are able to understand real vector space • Students are able to determine sub real vector spaces Students are able to determine linear combinations and linear free sets

√

√


5%

15,16

ETS

17-19 • Students are able to determine the basis and dimensions of a vector space

• Students are able to determine the relative coordinates of a vector against a base in a vector space

Students are able to determine row space, column space, empty space, rank, the nullity of a matrix

√

√

√


15%

20-22 Students are able to determine the transformation of the matrix from 𝑅 to 𝑅

Students are able to determine composition in matrix transformation

√

√


10%

23-25 • Students are able to determine the eigenvalues and eigenvectors of a square matrix • Students are able to determine the requirements for the matrix to be diagonalized and can diagonalize the matrix

√

√


10%

26-30 • Students are able to understand the results of deep times in real vector space • Students are able to understand the orthogonol set in the inner product space Students are able to form orthonormal bases by carrying out the gram-schmidt process

√

√

√


15%

31, 32

EAS

Number Questions 20

Percentage 100%

Information :






C6 : Creative

Assessment Criteria

1. Task (20%) After each chapter is taught the problem training is given 2. Quiz I (15%) Quiz I was held at the 4th week, the material from the beginning to the 4th week material with 5 questions with the same weight value 3. ETS (25%) ETS was held on the 8th week of the material from the beginning to the 7th week's material 4. Quiz II (15%) Quiz II was held at the 12th week, the material from after ETS reached the 12th week material with 5 questions with the same weight value 5. EAS (25%) EAS was held at the 16th week of material after ETS until the material at week 15

EXAMPLE OF QUIZ QUESTIONS 1. Complete the following system of linear equation with the Gaussian / Gauss Jordan elimination

𝑥 2𝑧 7𝑢 11 2𝑥 𝑦 3𝑧 4𝑢 9 3𝑥 3𝑦 𝑧 5𝑢 8

2𝑥 𝑦 4𝑧 4𝑢 10 2. Given the following system of linear equation

a. Determine the value of 𝑎 for the system of linear equation above to have one solution b. Determine the value of a for the system of linear equation above to have many solutions c. Determine the value of a for the system of linear equation above to have no one solution

3. Given 𝐴1 0 10 1 11 1 0

a. Determine 𝐴

b. Complete the linear equation 𝐴𝑋 𝐵 if 𝐵121

4. Determine

0 5 5 51

100 500

100 00

5. If 𝐴𝑎 𝑏 𝑐𝑑 𝑒 𝑓𝑔 ℎ 𝑖

and det 𝐴 = 4

a. Determine det 4𝐴

b. Determine 𝑎 𝑑 𝑎 𝑑 𝑔𝑏 𝑒 𝑏 𝑒 ℎ𝑐 𝑓 𝑐 𝑓 𝑖

SAMPLE HOW TO ASSESS NO 2

STEPS STEPS SKORI

Student able to make augmented matrix 1 2 33 1 54 1 𝑎 14

42

𝑎 2

4

II Students are able to use Elementary Linear Operations to change the augmented matrix into a lower triangle

matrix1 2 33 1 54 1 𝑎 14

42

𝑎 2𝑂𝐵𝐸 ∶ 𝐵 3𝐵 𝑎𝑛𝑑 𝐵 4𝐵

1 2 30 7 140 7 𝑎 2

410

𝑎 14𝑂𝐵𝐸: 𝐵 𝑥

1 2 30 1 20 7 𝑎 2

4107

𝑎 14𝑂𝐵𝐸 ∶ 𝐵 7𝐵

1 2 30 1 20 0 𝑎 16

4107

𝑎 4

4

III a. Students are able to determine the conditions for the above system of linear equation to have one solutionCondition : 𝑎 16 0 Answer : 𝑎 4, 4

4

IV b. Students are able to determine the conditions for the system of linear equation above to have many solutions

Condition : 𝑎 16 0 dan 𝑎 4 0 Answer : 𝑎 4

4

v c. Students are able to determine the conditions for the system of linear equation above to have no solutionsCondition : 𝑎 16 0 dan 𝑎 4 0 Answer : 𝑎 4

4

Study Program Name Bachelor, Mathematics Department, FMKSD-ITS

Course Name Elementary Linear Algebra

Course Code KM184203

Semester 2

Sks 4

Supporting Lecturer Dian Winda S, SSi, MSi

Materials

• Matrices and Vectors • Vector Space • Transformation

Learning Outcome




1. Students are able to follow developments and apply math and be able to communicate actively and correctly either oral or written

2. Students are able to explain intelligently and creatively about the significant role of ALE applications in the field of related knowledge clusters and other fields

3. Students have a special ability and able to process their ideas enough to support the next study in accordance with the related field

4. Students are able to present their knowledge in ALE independently or in teamwork


Breadth of Materials Learning Methods Time Estimatio

n

Student Learning

Experiences


Weighing

Assessment (%)

1-4

• Students are able to complete the SPL by the Gaussian or Gauss Jordan elimination method And able to explain why SPL has no settlement. • Students are able to use operations on the matrix and understand the algebraic properties of the matrix

• The understanding of SPL and Matrix is enlarged • Elementary Line Operation (OBE) • Gaussian and Gauss Jordan elimination • Operation Matrix • Properties of Algebra In Matrices . [Ref. 1 page: 9-98]

• Lectures, • Student conditioning, • Question and answer. • Giving exercise • Group discussion,

4x(2x50’)

TaSks Exercise questions

• Accuracy defines SPL and enlarged matrix. • Ability to complete SPL with OBE • Be able to complete SPL using Gaussian and Gauss Jordan • Be able to explain the properties of algebra in the matrix

15%

5-6 • Students are able to find inverse matrix, can complete SPL with inverse matrix • Students recognize the types of matrices and properties of the matrix

• Looking for Inverse matrix • Complete the SPL with the inverse matrix • Matrix type: Diagonal matrix, triangular matrix, symmetry matrix and its properties [Ref. 1 page: 99-139]


2x(2x50’)

TaSks Exercise questions

• Be able to get the inverse of a matrix • Able to complete SPL with inverse matrix • Be able to explain the types and properties of the matrix

5%

7-8 • Students are able to find the determinant of a matrix with Cofactor expansion • Students are able to find the determinant of a matrix by Row Reduction • Students are able to understand the properties of the determinant • Students are able to complete the SPL with the cramer's rules

• Counting determinants with Cofactor expansion • Counting determinants by Reducing Rows • the properties of the determinant • complete SPL with cramer rules [Ref. 1 page: 173-211]



• Able to calculate determinants with Cofactor expansion • Capable of Counting determinants by Row Reduction • Be able to explain the properties of the determinant • Able to complete SPL with cramer rules

10%

9-12 Students are able to understand the vectors in space 2, space 3 and space n and operation on the vector

Students are able to define norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry from linear System

vector in space 2, space 3 and space n

operation on the vector norm, dot product, distance, cross product, orthogonal set at R ^ n, set geometry of linear system [Ref. 1 page: 226-320]



Able to explain vectors in space 2, space 3 and space n

Be able to explain the operation on the vector

Ability to explain and norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry of linear System

15%

13,14 • Students are able to understand real vector spaces • Students are able to understand the real vector subspace • Students are able to understand linear and linearly independent combinations

• real vector space • real vector subspace • linear and linearly independent combinations [Ref. 1 page: 328-375]



• Be able to explain real vector spaces and real vector subspaces • Be able to explain linear combinations and linearly independent sets

5%

15,16 Midterm Exam

17-19 • Students are able to understand the basis and dimension of a vector space • Students are able to determine the relative coordinates of a vector on a basis in a vector space • Students are able to understand the row space, column space, blank space, rank, nullity of a matrix

• Base • The vector space dimension • Relative Coordinates • Transition Matrix • Classroom, Column Room, Empty Room • Rank and nullity [Ref. 1 page: 377-455]



• able to explain the basis and dimension of a vector space • able to determine the relative coordinates of a vector to a basis in a vector space • able to explain the row space, column space, empty space, rank, nullity of a matrix

15%

Reference Main :

20-22 Mahasiswa mampu memahami transformasi matriks dari 𝑅 ke 𝑅

Mahasiswa mampu memahami Komposisi pada transformasi matriks

Definition of matrix transformation from R ^ n to R ^ m and its types

How to get the Matrix Transformation

Composition on the transformation matrix

[Ref. 1 thing: 456-515]



The student is able to explain the matrix transformation from R ^ n to R ^ m

Students are able to explain Composition on matrix transformation

10%

23-25 • Students are able to determine the eigenvalues and eigenvectors of a square matrix • Students are able to determine the requirements of the matrix to be diagonalizable and can diagonalize the matrix

Eigenvalues Eigenvector Diagonalization of matrix A

with invertible matrix P so that D = P ^ (- 1) AP

[Ref. 1 page: 539-569]



• able to determine eigenvalues and eigenvectors of a square matrix • able to determine the requirement of the matrix to be diagonalizable and can diagonalize the matrix

10%

26-30 • Students are able to understand inner product results in real vector spaces • Students are able to understand the set of orthogonol in the inner product space • Students are able to form an orthonormal basis by performing the gram-schmidt process

• Understanding Inside Outcomes • the orthogonal set of inner product chambers • Gram-schmidt process [Ref. 1 page: 608-660]



• able to explain inner product results in real vector space • Students are able to explain the set of orthogonol in the inner product space • able to form an orthonormal basis by performing the gram-schmidt process

15%

31-32 FINAL EXAM


Supporting : 1. C.D. Meyer,”Matrix Analysis and Applied Linear Algebra”, SIAM, (2000) 2. Steven J. Leon, "Linear Algebra with Applications", Seventh Edition, Pearson Prentice Pagel, (2006). 3. Stephen Andrilli and David Hecker,”Elementary Linear Algebra, Fourth Edition”, Elsevier, (2010) 4. Subiono., ”Ajabar Linear”, Jurusan Matematika FMIPA-ITS, 2016.

Course

Course Name : Elementary Linear Algebra


Credit : 4

Semester : 2


Elementary Linear Algebra courses are a prerequisite for taking some of the next courses in the Department of Mathematics. Discussion topics include systems of linear equations and their solutions, matrix algebra, inverse matrices, determinants and n-dimensional real vector spaces including vector operations, norms of vectors, dot products on ℛ ,cross products on ℛ , basis, Row Space, Column Space, and Null Space, rank and nullity of the matrix, Matrix transformations, Eigenvalues, Eigenvectors and diagonalization of matrices, inner product spaces

Learning Outcome

[C2]




1. Students are able to follow developments and apply math and be able to communicate actively and correctly either oral or written

2. Students are able to explain intelligently and creatively about the significant role of ALE applications in the field of related knowledge clusters and other fields

3. Students have a special ability and able to process their ideas enough to support the next study in accordance with the related field

4. Students are able to present their knowledge in ALE independently or in teamwork

Main Subject

Systems of Linear Equations, Determinants, Real vector Space, Eigenvalues and Eigenvectors, Inner product spaces

Prerequisites

Reference



1. C.D. Meyer,”Matrix Analysis and Applied Linear Algebra”, SIAM, (2000)

2. Steven J. Leon, "Linear Algebra with Applications", Seventh Edition, Pearson Prentice Hall, (2006).

3. Stephen Andrilli and David Hecker,”Elementary Linear Algebra, Fourth Edition”, Elsevier, (2010)

4. Subiono., ”Ajabar Linier”, Jurusan Mathematics FMIPA-ITS, 2016

Study Program Name Bachelor, mathematics Department, FMKSD-ITS Course Name Function of Complex Variables Course Code KM184602 Semester 6 SKS 3 Supporting Lecturer Drs. Sentot Didik Surjanto, M.Si

Materials

• Complex numbers • Complex function

Learning Outcome



[C4]



1. Students are able to demonstrate, calculate and prove: the properties of complex number algebra, functions, limits, continuous, derivative, Cauchy-Riemann equations, analytic functions, harmonic functions.

2. Students are able to demonstrate, count and prove: elementary functions: exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, complex rank.

3. Students are able to demonstrate, calculate, prove and compare: complex path integrals, Cauchy-Goursat theorems, Cauchy integrals, theorems: Morera, Liouville, maximum modulus, Cauchy inequality.

4. Students are able to demonstrate, calculate, prove and compare series: rank, Taylor, Maclaurin, Laurent, series convergence.

5. Students are able to demonstrate, calculate, prove and compare: residual theorems and their uses.

6. Students are able to demonstrate, calculate, prove and compare: conformal transformation.



Student Learning

Experiences


Weighting

Assessment (%)

1,2 Students are able to explain the notion of complex numbers, the nature of algebra and its operations.

Lecture Contract o Understanding complex number systems o Notation of complex number forms o Operation of complex numbers o Basic concepts in topology in complex fields Ref: {1} Chapter 1 and Ref: {1} Chapter 1

o Lecture o Group discussion o Students work in front of the discussion result class

2x(3x50’)]

o Resume of course material o TaSks concerning complex numbers

o Able to solve problems about complex numbers o Understanding the notation of complex number forms with algebraic operations

10%

3 Students are able to explain the meaning of function, limit, continuous, derivative of complex functions.

Lecture Contract o Understanding complex functions o Limit and continuous complex functions o The derivation of complex functions Ref: {1} Chapter 2 and Ref: {2} Chapter 2


1x(3x50’)]

o Resume of course material o TaSks about complex functions

o Able to solve problems about function, limit, and continuous. o Understand the function derivative.

15%

4 Students are able to explain the meaning of Cauchy_Riemann equation, analytic function, harmonic.

Lecture Contract o Understanding the Cauchy_Riemann equation o Understanding of analytic functions o Understanding the harmonic function Ref: {1} Chapter 3 and Ref: {2} Chapter 3


1x(3x50’)] o Resume of course material o Duties on derivatives, analytic functions, harmonics

o Able to solve problems about the derivative o Understand the analytic function, harmonics

10%

5, 6 Students are able to explain elementary functions: exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and complex ranks

Lecture Contract o Understanding elementary functions o Understanding exponential functions, logarithms, trigonometry o Understanding trigonometric, hyperbolic and complex power inverse functions Ref: {1} Chapter 4 and Ref: {2} Chapter 4


2x(3x50’)] o Resume of course material o TaSks about elemental functions o Evaluate chapters 1 and 2

Able to solve problems about elementary functions

15%

7 Students are able to explain the integral complex functions: path integrals, Cauchy-Goursat theorem, Cauchy integral, Morera's theorem, Liouville's theorem

Lecture Contract o Understanding the integral of complex functions o Understanding the integrals of the trajectory o Understanding of Cauchy-Goursat's theorem, Cauchy integral, Morera's theorem, Liouville's theorem. Ref: {1} Chapter 5 and Ref: {2} Chapter 5


1x(3x50’)] o Resume of course material o The task of integral complex functions o Discuss evaluation chapters 1 and 2

Be able to solve problems about integral complex functions

15

8 MIDTERM EXAM

Reference Main : 1. Churchil, R., ”Complex Variables and Applications 8th edition”, McGraw-Hill, New York, 2009.

9, 10 Students are able to explain the power series: Taylor series, MacLaurin, Laurent, series operations

Lecture Contract o Understanding the power series o Understanding Taylor series, MacLaurin o Understanding Laurent, multiplication operations and the division of the series Ref: {1} Chapter 6 and Ref: {2} Chapter 6


2x(3x50’)] o Resume of course material o The task of power series

o Able to solve questions about power series

10%

11, 12, 13

Students are able to explain poles and residues: use of residues in integral.

Lecture Contract o Understanding poles and residues o Understanding the use of residues in integral o Integral notions of per unit circle, page disc and unnatural Ref: {1} Chapter 7 and Ref: {2} Chapter 7


3x(3x50’)] o Resume of course material o The task of using residues in integral

Be able to solve integral problems with residues

15%

14, 15 Students are able to explain the transformation of elinsnter and conformal functions.

Lecture Contract o Understanding the transformation of elementary functions o Understanding conformal transformation Ref: {1} Chapter 7,8 and Ref: {2} Chapter 7.8


2x(3x50’)] o Resume of course material o TaSks regarding the transformation of elinsnter and conformal functions

Able to solve problems of functional and conformal functional transformation

15%

16 Final Exam 10

2. Mathews, J.H, “Complex Variables for Mathematics and Engineering”, 6th edition, WM C Brown Publiser, Iowa, 2010.

Supporting : 1. Poliouras, J.D., Meadows D. S, ”Complex Variables for Scientists and Engineers 2nd edition ”, New York,

2014.


Course : Function of Complex Variables, Code: KM184602, sks: 3 sks, smt:6

Learning outcome:

1. Able to interpret basic mathematical concepts and compile evidence directly, indirectly, or with mathematical induction. 2. Able to identify simple problems, form mathematical models and solve them. 3. Mastering standard methods in the field of mathematics 4. Able to master the fundamental theory of mathematics which includes the concepts of set, function, differential, integral, space and mathematical structure. 5. Able to analyze the system and optimize its performance 6. Able to understand mathematical problems, analyze and solve them. 7. Able to analyze a phenomenon through a mathematical model and solve it 8. Able to explore, logical reasoning, generalization, abstraction, and formal evidence; 9. Able to observe, recognize, formulate and solve problems through a mathematical approach 10. Able to accept and follow new knowledge in accordance with the field of work being occupied

Meets


(Sub‐Competence)


Questions

Form of Assessment



1,2 Students are able to explain, calculate, prove the algebraic nature and operation of complex numbers.

√ √ √ 1 o Resume lecture materials

10%

o Task about complex numbers

3 Students are able to explain, calculate, prove the limit, continuous, derivative functions of complex functions.


o Tasks about complex functions

15%

4 Students are able to explain calculations, prove the Riemann Cauchy equation, analytic functions, harmonics.


o Tasks about derivatives, analytical, harmonic functions

10%

5, 6 Students are able to explain, calculate, prove elementary function equations: exponential, logarithmic, trigonometric, inverse trigonometry, hyperbolic and complex rank


o Tasks about elemental function

o Evaluation of chapters 1 and 2

15%

7 Students are able to explain, calculate, prove integral to complex functions: path integral, Cauchy-Goursat theorem, Cauchy integral, Morera theorem, Liouville theorem


o Tasks about complex

15

function integrals

o Discuss the evaluation of chapters 1 and 2

8 ETS

9, 10 Students are able to explain, calculate, prove rank series: Taylor series, MacLaurin, Laurent, series operations


o The task of the rank series

10%

11, 12, 13

Students are able to explain, calculate, prove poles and residues: the use of residues in integrals.


o The task of using residuals in integrals

15%

14, 15

Students are able to explain, calculate, prove the transformation of elementary and informal functions.

√ √ √ 3 o Resume of lecture material

o Tasks regarding transformations of elementary and conformal functions

15%

16 EAS

Number Questions Item 1 3 3 3 4 3 3 20

Percentage 5 15 15 15 20 15 15 20 100%

Informations :






C6 : Creative

Study Materials

• Number of complexes

• Complex function

Assessment Criteria

1. Task (20%)

Every finished chapter is taught 5 questions

2. Quiz I (15%)

After chapter 3 or 4 quizzes are given with 5 questions with the same weight

3. ETS (25%)

ETS is held on the 8th week of the material until the chapter that has been taught

4. Quiz II (15%)

It was held in the 12th week with the material after the ETS material until the material was given at the 12th week

5. EAS (25%)

EAS is held in the 16th week of the material after ETS until the conformal transformation chapter

TaskDesignFormatWeeks : 2 Tasks : 2

1. Purpose of Task: Students are able to calculate and prove complex roots

2. Description of Task: a. Claim object :

Determines the roots of complex numbers and prove the predetermined roots.

b. What to do and limitation : Determine the complex roots and prove the complexity of the complexity

c. Method/way of reference work used : The task is done on folio paper

d. Description of output of work produced / done: Understand the calculations and properties of the roots of complex numbers

1. If 𝑧 𝑎 𝑖𝑏 and 𝑤 𝑥 𝑖𝑦, show root 𝑧 that meets equation 𝑤 𝑧 is

𝑎2

12

𝑎 𝑏 1𝑎 √𝑎 𝑏

𝑏𝑖

3. Assessment criteria


1 Prove: 𝑤 𝑧 → 𝑥 𝑖𝑦 𝑎 𝑖𝑏

𝑥 𝑦 𝑖2𝑥𝑦 𝑎 𝑖𝑏

25

2 Then 𝑥 𝑦 𝑎

2𝑥𝑦 𝑏

25

3 Assume 𝑏 0 → 𝑦 substitute to

𝑥 𝑦 𝑎 → 𝑥𝑏

2𝑥𝑎

4𝑥 𝑏 4𝑎𝑥 → 𝑥 𝑎𝑥𝑏4

0

𝑥𝑎2

𝑎 𝑏4

0

25

4 So

𝑥𝑎2

𝑎 𝑏4

𝑎2

12

𝑎 𝑏

25

5 Since √𝑎 𝑏 , then the fulfillment is

𝑥𝑎2

12 𝑎 𝑏

6 Root from 𝑧 𝑎 𝑖𝑏 is

𝑎2

12

𝑎 𝑏 1𝑎 √𝑎 𝑏

𝑏𝑖

Score total 100

PlanofTest

TIU : Students are able to identify natural phenomena that have the form of nonlinear differential equations, analyze stability and periodic completion of the system [C3, A3]

No Topics & Sub Topics Number of Questions Total of

Questions Item Weight (%)

C2 C3 C4

1 2 3 4 5 6

1. Subject‐1 4 4 16

2. Subject‐2 2 2 8

3. Subject‐3 4 4 16

4. Subject‐4 4 4 16

5. Subject‐5 3 3 12

6. Subject‐6 3 3 12

7. Subject‐7 3 3 12

8 Subject‐8 2 2 8

Number of Questions Item: 10 15 25

Percentage (%): 40 60 100

No Special Learning Objectives (TIK) Number of Questions

C3C4 P3 P4 A3 A4

Total of Questions

Item

Weight%

1 2 3 4 4 5 6 7 8 9

1. TIK‐1 2 1 1 4 16

2. TIK‐2 1 1 2 8

3. TIK‐3 1 1 1 3 12

4. TIK ‐4 1 1 1 1 4 16

5. TIK ‐5 1 1 1 1 4 16

6. TIK ‐6 1 1 1 3 12

7. TIK ‐7 1 1 1 3 12

8 TIK‐8 1 1 2 8

Number of Questions Item: 3 7 4 2 4 5 25

Percentage (%): 12 28 16 8 16 20 100

ExampleofDescriptionTest

Questions :

1. Determine the root of √3 𝑖/

Answer:

√3 𝑖 2 𝑒𝑥𝑝 𝑖𝜋6 2𝑘𝜋 ; 𝑘 0, 1, ⋯

𝑐 √2 𝑒𝑥𝑝 𝑖𝜋

12 𝑘𝜋 ; 𝑘 0, 1


12 √2 𝑐𝑖𝑠 𝜋

12

𝑐𝑜𝑠𝛼2

1 cos 𝛼2

; 𝑠𝑖𝑛𝛼2

1 cos 𝛼2

𝑐𝑜𝑠𝜋

121 cos 𝜋/6

212 1

√32

2 √34

𝑠𝑖𝑛𝜋

121 cos 𝜋/6

212

1√32

2 √34

𝑐 √2 2 √3

4 𝑖2 √3

41

√22 √3 𝑖 2 √3

Since 𝑐 𝑐 , the root of √3 𝑖 is 1

√22 √3 𝑖 2 √3

ScoreGuidelines


1 Able to calculate modulus and complex number arguments

√3 𝑖 2 𝑒𝑥𝑝 𝑖𝜋6

2𝑘𝜋 ; 𝑘 0, 1, ⋯


12𝑘𝜋 ; 𝑘 0, 1


12 √2 𝑐𝑖𝑠𝜋

12

30

2 Able to prove trigonometric equations

𝑐𝑜𝑠𝛼2

1 cos 𝛼2

; 𝑠𝑖𝑛𝛼2

1 cos 𝛼2

𝑐𝑜𝑠𝜋

121 cos 𝜋/6

212

1√32

2 √34

𝑠𝑖𝑛𝜋

121 cos 𝜋/6

212

1√32

2 √34

40

3 Able to count and substitute complex numbers in exponential form

𝑐 √2 2 √3

4𝑖

2 √34

1√2

2 √3 𝑖 2 √3

Since 𝑐 𝑐 , then root from √3 𝑖 is 1

√22 √3 𝑖 2 √3

30

100

Study Program Name Bachelor, mathematics Department, FMKSD-ITS Course Name Complex Variable Course Code KM184602 Semester 6 SKS 3 Supporting Lecturer Drs. Sentot Didik Surjanto, M.Si

Materials

• Complex numbers • Complex function

Learning Outcome



[C4]



1. Students are able to explain the nature of algebra in complex numbers, determine limits, continuity and derivation of complex functions and can explain the properties of elementary functions: exponential functions, logarithms, and trigonometry, hyperbolic functions, and trigonometric invers

2. Students are able to calculate the integral complex functions using appropriate properties and theorems

3. Students are able to explain the mapping / transformation by elementary functions and conformal mapping / transformation

4. Students are able to explain the residual theorem and its use to compute the integral complex functions

5. Students are able to investigate series convergence, decompose complex functions in power series, Taylor, Maclaurin and Lourent series



Student Learning

Experiences


Weighting

Assessment (%)

1,2 Students are able to explain the notion of complex numbers, the nature of algebra and its operations.

Lecture Contract o Understanding complex number systems o Notation of complex number forms o Operation of complex numbers o Basic concepts in topology in complex fields Ref: {1} Chapter 1 and Ref: {1} Chapter 1


2x(3x50’)]

o Resume of course material o TaSks concerning complex numbers

o Able to solve problems about complex numbers o Understanding the notation of complex number forms with algebraic operations

10%

3 Students are able to explain the meaning of function, limit, continuous, derivative of complex functions.

Lecture Contract o Understanding complex functions o Limit and continuous complex functions o The derivation of complex functions Ref: {1} Chapter 2 and Ref: {2} Chapter 2


1x(3x50’)]

o Resume of course material o TaSks about complex functions

o Able to solve problems about function, limit, and continuous. o Understand the function derivative.

15%

4 Students are able to explain the meaning of Cauchy_Riemann equation, analytic function, harmonic.

Lecture Contract o Understanding the Cauchy_Riemann equation o Understanding of analytic functions o Understanding the harmonic function Ref: {1} Chapter 3 and Ref: {2} Chapter 3


1x(3x50’)] o Resume of course material o Duties on derivatives, analytic functions, harmonics

o Able to solve problems about the derivative o Understand the analytic function, harmonics

10%

5, 6 Students are able to explain elementary functions: exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and complex ranks

Lecture Contract o Understanding elementary functions o Understanding exponential functions, logarithms, trigonometry o Understanding trigonometric, hyperbolic and complex power inverse functions Ref: {1} Chapter 4 and Ref: {2} Chapter 4


2x(3x50’)] o Resume of course material o TaSks about elemental functions o Evaluate chapters 1 and 2

Able to solve problems about elementary functions

15%

7 Students are able to explain the integral complex functions: path integrals, Cauchy-Goursat theorem, Cauchy integral, Morera's theorem, Liouville's theorem

Lecture Contract o Understanding the integral of complex functions o Understanding the integrals of the trajectory o Understanding of Cauchy-Goursat's theorem, Cauchy integral, Morera's theorem, Liouville's theorem. Ref: {1} Chapter 5 and Ref: {2} Chapter 5


1x(3x50’)] o Resume of course material o The task of integral complex functions o Discuss evaluation chapters 1 and 2

Be able to solve problems about integral complex functions

15

8 MIDTERM EXAM

Reference Main : 1. Churchil, R., ”Complex Variables and Applications 8th edition”, McGraw-Hill, New York, 2009.

9, 10 Students are able to explain the power series: Taylor series, Maclaurin, Laurent, series operations

Lecture Contract o Understanding the power series o Understanding Taylor series, Maclaurin o Understanding Laurent, multiplication operations and the division of the series Ref: {1} Chapter 6 and Ref: {2} Chapter 6


2x(3x50’)] o Resume of course material o The task of power series

o Able to solve questions about power series

10%

11, 12, 13

Students are able to explain poles and residues: use of residues in integral.

Lecture Contract o Understanding poles and residues o Understanding the use of residues in integral o Integral notions of per unit circle, pagef disc and unnatural Ref: {1} Chapter 7 and Ref: {2} Chapter 7


3x(3x50’)] o Resume of course material o The task of using residues in integral

Be able to solve integral problems with residues

15%

14, 15 Students are able to explain the transformation of elinsnter and conformal functions.

Lecture Contract o Understanding the transformation of elementary functions o Understanding conformal transformation Ref: {1} Chapter 7,8 and Ref: {2} Chapter 7.8


2x(3x50’)] o Resume of course material o TaSks regarding the transformation of elinsnter and conformal functions

Able to solve problems of functional and conformal functional transformation

15%

16 Final Exam 10


Supporting : 1. Poliouras, J.D., Meadows D. S, ”Complex Variables for Scientists and Engineers 2nd edition ”, New York,

2014.

Course

Course Name : Complex Variable


Credit : 3

Semester : 6


The subjects of the complex function variables address the problem: complex numbers, complex mapping, limiting, continuous, derivative, complex integral, Green Theorem, Cauchy, Morera and Liouvile, convergence / divergence sequences and series, singularities, residual theorems and their use in complex integrals, conformal mapping.

Learning Outcome

[C2]



[C4]



1. Students are able to explain the nature of algebra in complex numbers, determine limits, continuity and derivation of complex functions and can explain the properties of elementary functions: exponential functions, logarithms, and trigonometry, hyperbolic functions, and trigonometric invers

2. Students are able to calculate the integral complex functions using appropriate properties and theorems

3. Students are able to explain the mapping / transformation by elementary functions and conformal mapping / transformation

4. Students are able to explain the residual theorem and its use to compute the integral complex functions

5. Students are able to investigate series convergence, decompose complex functions in power series, Taylor, Maclaurin and Lourent series

Main Subject

Complex number system, complex variable function, limit, continuity, derivative, analytic function and harmonic function, elementary functions: exponential, logarithm, trigonometry, hyperbolic, and trigonometric inverse, complex integration, contour, theorem: Green, Cauchy, Morera and Liouvile, convergence / divergence sequence and series, singularity, residual theorem and its use in complex function integral, conformal mapping

Prerequisites

Analysis I

Reference

1. Churchil, R., ”Complex Variables and Applications 8th edition”, McGraw-Hill, New York, 2009.



1. Poliouras, J.D., Meadows D. S, ”Complex Variables for Scientists and Engineers 2nd edition ”, New York, 2014.

Study Program Name Bachelor, Mathematics Department,FMKSD-ITS Course Name Introduction to Dynamic Optimization Course Code KM184716Semester 7 Sks 2 Supporting Lecturer Dr. Dra. Mardlijah,MT

Materials

Calculus of Variatons Optimal Control

Learning Outcome


[C4]




. 1. Students are able to follow the development and apply Mathematics and able

to communicate actively and correctly either oral or written. 2. Students are able to explain basic and advanced principles of the Theory they

understand especially in relation to the optimization design formulation and the method of completion

3. Students are able to explain intelligently and creatively about the significant role of the optimization system in the field of related knowledge clusters or other fields.



Student Learning

Experiences



(%)

1 Students are able to model and categorize static and dynamic optimization problems.

Lecture Contract Static and Dynamic optimization [1]: Subchan Chapter II

Propaedeutics , simple case study

1x(2x50”)

Writing about the solution of some given problems

Good ability to explain differences in static and dynamic optimization problems and apply them

10 %

2,3 Student are ablet to differentiate simple function and functional problems

Function and Functional differences

[1]: Naidu Chapter II [2]: Krasnov Chapter II

‐ Lectures ‐ Exercises/Review

2x(2x50”)


Able to understand function and functional differences

15%

4 Students are able to explain the concepts of optimal function and functional

Optimal function and functional [1]: Naidu Chapter II.2

‐ Lectures ‐ Exercise

1x(2x50”)


Good ability to explain the concept of optimal function and functional

5 %

5-6-7 Students are able to explain the basics of variational and classify the real problems into Euler-Lagrange cases

Know time and state Decrease in Euler-Lagrange The Euler-Lagrange Cases [1]: Naidu Chapter II.3


3x(2x50”)


Good ability to explain basic of variational and decrease of Euler-Lagrange

20%

MIDTERM EXAM

9,10

Students are able to explain and evaluate optimal function and functional with constraints

Optimal function and functional with constraints [1]: Naidu Chapter II.5-II.6

‐ Lectures, ‐ Review, ‐ Practice

2x(2x50”)


Good ability to explain the difference between array-based and linked stack implementation

10%

11-12-13

Students are able to apply variational approach to optimal control and evaluate it

Cariational approach to optimal control [1]: Naidu Chapter II.7-II.8

‐ Lectures ‐ Review, ‐ Practice

3x(2x50”)

‐ Source code of practice result

‐ Writing about the solution of

Good ability to apply a variational approach to optimal control and to evaluate

15%

Reference Main : 1. Naidu, D.S, Optimal Control Systems, CRC Press, 2002 2. Bolza, O. Lectures on the Calculus of Variations, American Mathematical Society; 3 edition (October 31,

2000)

Supporting : 1. Subchan, S and Zbikowski, R., Computational Optimal Control: Tools and Practice, Wiley, 2009.

some given problems

14-15

Students are able to explain, apply optimal control in real problem and evaluate the result

Case study Lectures Project I

2x(2x50”)

Presentation

Good ability to explain, apply optimal control in real problems and evaluate results

25%

(16) Final Exam


Course : Introduction to Dynamic Optimization, Code: KM184716, sks:2 sks, smt:7

Learning outcome :

1. Able to identify simple problems, form mathematical models and solve them. 2. Able to identify problems, form mathematical models and solve them. 3. Able to analyze the system and optimize its performance 4. Able to understand mathematical problems, analyze and solve them. 5. Able to analyze a phenomenon through a mathematical model and solve it 6. Able to apply mathematical thinking to solve optimization problems both analytically and empirically. 7. Able to observe, recognize, formulate and solve problems through mathematical approaches 8. Able to analyze structurally a system / problem, reconstruct, and modify it into a mathematical model;

Meets


(Sub‐Competence)


Questions

Form of Assessment



1 Students are able to model categorizing static and dynamic optimization problems.

v v v Write about the solutions to some of the problems given

10%

2,3 Students are able to model categorizing static and dynamic optimization problems.

v v v Write about the solutions to some

15%

of the problems given

4 Students are able to explain the concept of optimal function and function


5%

5,6,7

- Students are able to explain variational basics and classify real problems into Euler-Lagrange cases


20%

8 Mid Semester Evaluation

9‐10

Students are able to explain and evaluate optimal functions and functional constraints

v v v - Writing about solutions to several problems given

10%

11, 12, 13


v v v - Writing about solutions to several problems given

15%

14,15

- Students are able to explain and apply optimal control in real problems and evaluate the results

v v v o Presentation 25%

16 Final Semester Evaluation

Number Questions Item

Percentage 100%

Informations :






C6 : Creative

Task Design Format

Course : Introduction to Dynamical Optimization Semester : VII Code : KM184716 sks : 2 Weeks : 4 1. Purpose of Task :

Students are able to explain the concept of optimal function and function

2. Task Description a. Claim Object :

Function optimization and simple functional forms

b. What to do and limitation : B1. Determine whether the following functions are maximum or minimum

𝑓 𝑥 𝑦 2𝑥 4𝑥𝑦 2𝑦 B2. Find distance between curve 𝑦 𝑥 and 𝑦 𝑥 on interval 0,1 B3. Determine extreme conditional from 𝑓 𝑥𝑦𝑧 with condition

𝑥 𝑦 𝑧 5 𝑥𝑦 𝑦𝑧 𝑧𝑥 8

B4. Determine change in functional

𝐽 𝑦 𝑥 𝑦 𝑥 𝑦 𝑑𝑥

if given 𝑦 𝑥 𝑒 dan 𝑦 𝑥 1.

c. Method/way reference work used : Tasks are typed in A4 paper size 12 letter spacing 1.15 normal margins.

d. Description of output of work produced/ done Writing about the solutions to several problems given

3. Assessment criteria No. Assessed Aspects / Concepts Score

1 Able to determine optimization (maximum and minimum values) of a function

15

2 Able to determine the distance between two functions 25

3 Able to determine extreme conditionals of functions 𝑓 𝑥𝑦𝑧 with a constraint

25

4 Able to determine changes in functional J [y (x)] with an constraint

35

Score total 100

Task Design Format

Course : Introduction to Dynamical Optimization Semester : VII Code : KM184716 sks : 2 Weeks : 12 1. Purpose of Task :


2. Description of Task a. Claim object:

Functional

b. What to do and limitation: B1. Determine completion from problem follows: (score 30%)

𝐽 𝑥 𝑡 𝑡𝑥 𝑥 𝑑𝑡

B2. Determine completion from the following dynamics optimization problems: (score 35%)

min 𝐽 𝑢 𝑡12

𝑥 𝑢 𝑑𝑡

with constraints 𝑥 𝑢

𝑥 0 1 B3. Determine completion from the following dynamical optimization problem:

(score 35%)

max 𝐽 𝑢 𝑡 𝑢 𝑑𝑡

with contraints 𝑥 𝑥 𝑢 𝑥 0 1 𝑥 1 0

c. Method/way the reference works is used:

Tasks are typed in A4 paper size 12 letter spacing 1.15 normal margins.

d. Description of output of work produce/done : Write about the solutions to some of the problems given

Study Program Name Bachelor, Mathematics Department,FMKSD-ITS Course Name Introduction to Dynamic Optimization Course Code KM184716Semester 7 Sks 2 Supporting Lecturer Dr. Dra. Mardlijah,MT

Materials

Calculus of Variatons Optimal Control

Learning Outcome


[C4]




. 1. Students are able to follow the development and apply Mathematics and able

to communicate actively and correctly either oral or written. 2. Students are able to explain basic and advanced principles of the Theory they

understand especially in relation to the optimization design formulation and the method of completion




Student Learning

Experiences



(%)

1 Students are able to model and categorize static and dynamic optimization problems.

Lecture Contract Static and Dynamic optimization [1]: Subchan Chapter II

Propaedeutics , simple case study

1x(2x50”)


Good ability to explain differences in static and dynamic optimization problems and apply them

10 %

2,3 Student are ablet to differentiate simple function and functional problems

Function and Functional differences

[1]: Naidu Chapter II [2]: Krasnov Chapter II

‐ Lectures ‐ Exercises/Review

2x(2x50”)


Able to understand function and functional differences

15%

4 Students are able to explain the concepts of optimal function and functional

Optimal function and functional [1]: Naidu Chapter II.2


1x(2x50”)


Good ability to explain the concept of optimal function and functional

5 %

5-6-7 Students are able to explain the basics of variational and classify the real problems into Euler-Lagrange cases

Know time and state Decrease in Euler-Lagrange The Euler-Lagrange Cases [1]: Naidu Chapter II.3


3x(2x50”)


Good ability to explain basic of variational and decrease of Euler-Lagrange

20%

MIDTERM EXAM

9,10

Students are able to explain and evaluate optimal function and functional with constraints

Optimal function and functional with constraints [1]: Naidu Chapter II.5-II.6

‐ Lectures, ‐ Review, ‐ Practice

2x(2x50”)


Good ability to explain the difference between array-based and linked stack implementation

10%

11-12-13

Students are able to apply variational approach to optimal control and evaluate it

Cariational approach to optimal control [1]: Naidu Chapter II.7-II.8

‐ Lectures ‐ Review, ‐ Practice

3x(2x50”)

‐ Source code of practice result

‐ Writing about the solution of

Good ability to apply a variational approach to optimal control and to evaluate

15%

Reference Main : 1. Naidu, D.S, Optimal Control Systems, CRC Press, 2002 2. Bolza, O. Lectures on the Calculus of Variations, American Mathematical Society; 3 edition (October 31,

2000)

Supporting : 1. Subchan, S and Zbikowski, R., Computational Optimal Control: Tools and Practice, Wiley, 2009.

some given problems

14-15

Students are able to explain, apply optimal control in real problem and evaluate the result

Case study Lectures Project I

2x(2x50”)

Presentation

Good ability to explain, apply optimal control in real problems and evaluate results

25%

(16) Final Exam

Course

Course Name : Introduction to Dynamic Optimization


Credit : 2

Semester : 7


The discussion of the dynamic optimization course includes the study of the basics of calculus variation, and the approach of calculus varasi on optimal control. In the learning process in the classroom learners will learn to identify problems, model. In addition to being directed to independent learning through tasks, learners are directed to cooperate in group work.

Learning Outcome


[C4]




1. Students are able to follow the development and apply Mathematics and able to communicate actively and correctly either oral or written.

2. Students are able to explain basic and advanced principles of the Theory they understand especially in relation to the optimization design formulation and the method of completion


Main Subject

Basic Concepts, Function and Functional, Optimum of a Function and a Functional, The Basic Variational Problem, Fixed-End Time and Fixed-End State System, Discussion on Euler-Lagrange Equation , Different Cases for Euler-Lagrange Equation, The Second Variation , Extrema of Functions with Conditions, Extrema of Functionals with Conditions, Variational Approach to Optimal Control Systems.

Prerequisites

Reference

1. Naidu, D.S, Optimal Control Systems, CRC Press, 2002 2. Bolza, O. Lectures on the Calculus of Variations, American Mathematical

Society; 3 edition (October 31, 2000)


1. Subchan, S and Zbikowski, R., Computational Optimal Control: Tools and Practice, Wiley, 2009.

1

Study Program Name Bachelor, mathematics Department, FMKSD-ITS Course Name Statistical Methods Course Code KM184305

Semester 3 Sks 3

Supporting Lecturer Dra. Farida A.W., MS / Drs. Sentot D.S., M.Si / Dra. Nuri Wahyuningsih, M.Kes

Materials

• Descriptive Statistics • Distribution of random variables • Discrete and continuous special contributions • Distribution of average sampling • Guess hose of a parameter • Hypothesis Testing • Regression Analysis

Learning Outcome

[C2]




1. Able to calculate, prove and apply random variable distribution 2. Being able to separate, connect, compare the distribution of discrete and

continuous random variables 3. Able to calculate special distribution opportunities, both discrete and

continuous, by looking at tables 4. Able to calculate and compare the average sampling distribution 5. Able to calculate and compare estimated hoses for distribution parameters

and test distribution parameters 6. Able to calculate and compare simple linear regression models

2



Student Learning

Experiences


Weighting

Assessment (%)

1-3 Mahasiswa mampu • Calculate the mode, median, average and variance of a data

• Lecture Contract • Understanding statistics • Source, type and how to get data. • Data scale and sum notation. • Presentation of data • Statistical measurements for data include the measure of centralization, deployment, and the size of the spurt. [Ref. 2 pp: 1-19, 4 things: 1-10, 25-26] [Ref. 2 pp: 47-63, 4 pp: 13-24] [Ref. 2 pp: 21-45,57-63, 4 pp: 27-47]

• Lectures, • Group discussion, Task 1 : • Literature review, • Do a resume from literature review,

3x(2x50’)

Non-Tests: Lecture notes

Understand the content of the course

15 %

3

4-6 Mahasiswa mampu Describes and

determines the distribution of discrete random variables

• The definition of random variables • Opportunity distribution of random variables • Average and variance of the opportunity distribution [Ref. 1 pp: 34-41, 2 pp: 114- 142 4 things: 108-113]

• Lectures, • Group discussion, Task-2: • Literature review, • Conduct a resume from literature review,

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7-9 Mahasiswa mampu calculate specific

distribution opportunities, either discrete or continuous, by looking at the tables

• Distribution of Discrete Opportunities ie Uniform, Binomial, Multinomial, Binomial Negative, Geometric, Hipergeometric and Poisson. • Distribution of Continuous Opportunities ie Uniform, Normal, Chi-Square, t and F. [Ref. 1 thing: 90-112,120-144, 2 pp: 152-173, 180- 196, 3 pp: 108-


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4

119, 4 pp: 145-159, 193- 208]

10-11 Midterm Exam

12-14 Mahasiswa mampu explain and define the

average sampling distribution

• Average Sampling Distribution • Distribution Approach t • Distribution of Average Difference Sampling [Ref.1 pp: 173 - 202 2 pp: 206-235]


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15-17 Mahasiswa mampu determine the alleged

hose for the distribution parameters and test the distribution parameters

• Good predictor characteristics. • Alleged hose for average parameters and variants • Sample size. • Understanding of statistical hypotheses, type I and II errors • Test of average parameters and variance • Uncertainty test. [Ref. 1 pp: 256-291, 2 pp: 287-337, 4 pp: 255-275]


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5

Reference Main : 1. Walpole, R.E, Pengantar statistika, edisi 3, Gramedia, Jakarta, 2002 2. Walpole, R.E, Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan, edisi 3, ITB, Bandung, 2000 3. Gouri, BC., Johnson RA, Statistical Concepts and Methods, John Wiley and Sons, New York, 1977 4. Walpole, RE, ProChapterility and Statistics for Engineer and Scientis, , 2016

Supporting :

1. Draper NR, Smith H., Analisis Regresi Terapan, Gramedia, Jakarta, 1992 2. Spiegel RM, ProChapterility and Statistics, Kin Keong Print, Singapore, 1985


Course : Statistical Method, Code: KM184305, sks: 3 sks, smt:3

18-21 Mahasiswa mampu • Calculate and compare estimates and testing parameters for simple linear regression models

• Understanding regression and correlation. • Estimation and testing of Model parameters. • Testing model assumptions.[Ref.1 pp: 300-329, 2 pp: 340-361, 6 pp: 1-51, 135-169]


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22-24 Final Exam

6

Learning Outcome:

1. Able to interpret basic mathematical concepts and compile evidence directly, indirectly, or with mathematical induction.

2. Able to identify simple problems, form mathematical models and solve them.

3. Mastering standard methods in the field of mathematics

4. Able to master the fundamental theory of mathematics which includes the concepts of set, function, differential, integral, space and

mathematical structure.

5. Able to analyze a phenomenon through a mathematical model and solve it

6. Able to observe, recognize, formulate and solve problems through mathematical approaches

7. Able to assess the accuracy of mathematical models and interpret them

8. Able to utilize various alternative mathematical problem solving that has been available independently or in groups for the right decision

making

Mee

ts

Spesific Learning Objective

(Sub‐Competence)

Elements of Competency in Assessment Questio

ns number

Form of Assessment



1-3 Students are capable

Able to calculate, prove and apply random variable distribution

√ √ √ 3 Non-Test: Lecture note

15 %

7

4-6 Students are capable • Calculate and apply the average and variants of the discrete random variable opportunity distribution


15 %


• calculate special distribution opportunities, both discrete and continuous, by looking at tables


15%

10‐11

ETS


• Calculate and compare the average sampling distribution


15%


• Calculate the estimated interval for distribution parameters and test the distribution parameters


25%


• Calculate and compare estimates and testing parameters for simple linear regression models


15%

22‐24

EAS

Numbers Item Question √ √ √ 5

Percentage 100%

Informations :


8





C6 : Creative

• Descriptive Statistics • Distribution of random variables • Discrete and continuous special contributions • Average sampling distribution • Estimated interval for a parameter • Hypothesis Test • Regression Analysis

Assessment Criteria

1. Task (20%)

Every finished chapter is taught 5 questions

2. Quiz I (15%)

After chapter 3 or 4 quizzes are given with 5 questions with the same weight

3. ETS (25%)

ETS is held on the 8th week of material until the chapter

4. Quiz II (15%)

9

Conducted at 12th week with material after ETS material until the 12th week

5. EAS (25%)

EAS was held at the 16th week of material after ETS until the regression chapter

FormatofTaskDesign

Course : Statistical Method

Semester : III (Tiga)

Code : KM184305 sks : 3

Week‐ : 3 Task : 3

1. Task Goal : Students are able to determine the mean, variant distribution of variables and opportunities

2. Task Description a. Object :

Determine the sample space of all occurrences of an experiment, determine the distribution of variable 𝑋 and calculate the probability of variable

𝑋

b. What to do and limitation : Determine sample space and calculate probability of variable 𝑋

c. Method used : Task is done in folio paper

d. Description of task output that has done : Completion according to the chapter that has been taught

1. The success of someone entering the CPNS test is 0.4, if 15 people take the test, how many opportunities:

a. At least 10 people succeeded

10

b. There are 3‐8 people who succeed

c. Right 5 people who succeed

d. With Chebyshev's argument, determine and interpret the interval 𝜇 2𝜎

3. Question and evaluation criteria


1 Answer a:

At least 10 people succeeded

Let 𝑋 is people that succeeded, than 𝑃 𝑋 10 1 𝑃 𝑋 10

1 𝑏 𝑥; 15, 0.4

1 0,9662 0,0338

25

2 Answer b:

There are 3‐8 people succeed

𝑃 3 𝑋 8 𝑏 𝑥; 15, 0.4

𝑏 𝑥; 15, 0.4 𝑏 𝑥; 15, 0.4

0,9050 0,0271 0,8779

25

3 Answer c: 25

11

Right 5 people who succeed

𝑃 𝑋 5 𝑏 5; 15, 0.4

𝑏 𝑥; 15, 0.4 𝑏 𝑥; 15, 0.4

0,4032 0,2173 0,1859

4 Answer d:

With Chebyshev's argument, determine and interpret the

interval 𝜇 2𝜎

Is a binomial experiment with:

𝑛 15; 𝑝 0,4 → 𝜇 15 ∙ 0,4 6 𝑑𝑎𝑛 𝜎 15 ∙ 0,4 ∙ 0,63,6 → 𝜎 3,6 1,897

So 𝜇 2𝜎 6 2 ∙ 1,897 or from 2,206 to 9,794. Dari

Chebyshev states that the number of successful tests

among 15 participants is between 2,206 to 9,794 with at

least opportunities ¾.

25

Score Total 100

12

TestPlanning

TIU : Students are able to identify natural phenomena which are examples of statistical method problems [C3,A3]

No Subject and Sub‐topic Question Numbers Total Questions Weights

(%) C2 C3 C4

1 2 3 4 5 6

1. Subjet‐1 4 4 16

2. Subject‐2 2 2 8

3. Subject‐3 4 4 16

4. Subject‐4 4 4 16

5. Subject‐5 4 4 16

6. Subject‐6 4 4 16

7. Subject‐7 3 3 12

Number of item questions: 10 15 25

Percentage (%): 100 100

No Special Learning Objectives (TIK) Questions Number

13

C3 C4 P3 P4 A3 A4 Question Numbers

Weight%

1 2 3 4 4 5 6 7 8 9

1. TIK‐1 2 1 1 4 16

2. TIK‐2 1 1 2 8

3. TIK‐3 1 1 2 4 16

4. TIK ‐4 1 1 1 1 4 16

5. TIK ‐5 1 1 1 1 4 16

6. TIK ‐6 2 1 1 4 16

7. TIK ‐7 1 1 1 3 12

Number of item questions: 3 7 4 2 4 5 25

Percentage (%): 12 28 16 8 16 20 100

14

ExampleDescriptionTest

Question :

1. A balanced dice is thrown twice. If X states how many times the number 4 appears and Y states how many times the number 6 appears from the two

throws, specify:

a. Shared distribution for X and Y b. Calculate 𝑃 𝑋, 𝑌 ∈ 𝐴 for 𝐴 𝑋, 𝑌 |𝑥 2𝑦 3

Answer a:

f(X,Y) X

Total h(y) 0 1 2

Y

0 16/36 8/36 1/36 25/36

1 8/36 2/36 0 10/36

2 1/36 0 0 1/36

Total g(x) 25/36 10/36 1/36 1

𝑔 0 𝑃 𝑋 0 𝑓 0,0 𝑓 0,1 𝑓 0,21636

836

136

2536

𝑔 1 𝑃 𝑋 11036 , 𝑔 2 𝑃 𝑋 2

136

ℎ 0 𝑃 𝑌 0 𝑓 0,0 𝑓 0,1 𝑓 0,21636

836

136

2536

ℎ 1 𝑃 𝑌 11036

; ℎ 2 𝑃 𝑌 21

36

15

table the Marginal is:

X 0 1 2

𝑔 𝑋 25/36 10/36 1/36

Y 0 1 2

ℎ 𝑌 25/36 10/36 1/36

Answer b:

𝑃 𝑋, 𝑌 ∈ 𝐴 𝑋, 𝑌 |𝑥 2𝑦 3 ; 𝑥 0, 1, 2 𝑑𝑎𝑛 𝑦 0, 1, 2

𝑓 0,0 𝑓 0,1 𝑓 1,0 𝑓 1,1 𝑓 2,01636

836

836

236

136

3536

ScoringGuidelines

No. Assessed Aspects / Concepts Skor

1 Able to make a shared distribution table of 2 variables as shown in

the answers a. and calculation

𝑔 0 𝑃 𝑋 0 𝑓 0,0 𝑓 0,1 𝑓 0,21636

836

136

2536

𝑔 1 𝑃 𝑋 11036 , 𝑔 2 𝑃 𝑋 2

136

30

16

ℎ 0 𝑃 𝑌 0 𝑓 0,0 𝑓 0,1 𝑓 0,21636

836

136

2536

ℎ 1 𝑃 𝑌 11036

; ℎ 2 𝑃 𝑌 21

36

2 Able to make marginal tables from each variable

a 𝑔 𝑥 ; 𝑥 0, 1, 2

𝑔 02536 ; 𝑔 1

1036 ; 𝑔 2

136

15

b ℎ 𝑦 ; 𝑦 0, 1, 2

ℎ 02536

; ℎ 11036

; ℎ 21

36

15

3 Able to calculate opportunities along with the construction of

definitions given

𝑃 𝑋, 𝑌 ∈ 𝐴 𝑋, 𝑌 |𝑥 2𝑦 3 ; 𝑥 0, 1, 2 𝑑𝑎𝑛 𝑦 0, 1, 2 𝑓 0,0 𝑓 0,1 𝑓 1,0 𝑓 1,1 𝑓 2,0

1636

836

836

236

136

3536

40

Score total 100

1

Study Program Name Bachelor, mathematics Department, FMKSD-ITS Course Name Statistical Methods Course Code KM184305

Semester 3 Sks 3

Supporting Lecturer Dra. Farida A.W., MS / Drs. Sentot D.S., M.Si / Dra. Nuri Wahyuningsih, M.Kes

Materials

• Descriptive Statistics • Distribution of random variables • Discrete and continuous special contributions • Distribution of average sampling • Guess hose of a parameter • Hypothesis Testing • Regression Analysis

Learning Outcome




1. Students are able to understand simple statistical problems, analyze with statistical basic

methods, and solve them. 2. Students are able to identify data, analyze it using appropriate basic statistical methods, present

it orally and written in academic way. 3. Students are able to be responsible for the conclusions drawn based on data and methods which

have learnt during the course.

2



Student Learning

Experiences


Weighting

Assessment (%)

1-3 Mahasiswa mampu explain and apply

descriptive statistics

• Lecture Contract • Understanding statistics • Source, type and how to get data. • Data scale and sum notation. • Presentation of data • Statistical measurements for data include the measure of centralization, deployment, and the size of the spurt. [Ref. 2 things: 1-19, 4 things: 1-10, 25-26] [Ref. 2 things: 47-63, 4 things: 13-24] [Ref. 2 things: 21-45,57-63, 4 things: 27-47]

• Lectures, • Group discussion, Task 1 : • Literature review, • Do a resume from literature review,

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15 %

3

4-6 Mahasiswa mampu Describes and

determines the distribution of discrete random variables

• The definition of random variables • Opportunity distribution of random variables • Average and variance of the opportunity distribution [Ref. 1 thing: 34-41, 2 things: 114- 142 4 things: 108-113]


3x(2x50’)




7-9 Mahasiswa mampu calculate specific

distribution opportunities, either discrete or continuous, by looking at the tables

• Distribution of Discrete Opportunities ie Uniform, Binomial, Multinomial, Binomial Negative, Geometric, Hipergeometric and Poisson. • Distribution of Continuous Opportunities ie Uniform, Normal, Chi-Square, t and F. [Ref. 1 thing: 90-112,120-144, 2 things: 152-173, 180- 196, 3 things:


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4

108-119, 4 things: 145-159, 193- 208]

10-11 Midterm Exam

12-14 Mahasiswa mampu explain and define the

average sampling distribution

• Average Sampling Distribution • Distribution Approach t • Distribution of Average Difference Sampling [Ref.1 pp: 173 - 202 2 things: 206-235]


3x(2x50’)




15-17 Mahasiswa mampu determine the alleged

hose for the distribution parameters and test the distribution parameters

• Good predictor characteristics. • Alleged hose for average parameters and variants • Sample size. • Understanding of statistical hypotheses, type I and II errors • Test of average parameters and variance • Uncertainty test. [Ref. 1 thing: 256-291, 2 things: 287-337, 4 things: 255-275]


3x(2x50’)




5

Reference Main : 1. Walpole, R.E, Pengantar statistika, edisi 3, Gramedia, Jakarta, 2002 2. Walpole, R.E, Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan, edisi 3, ITB, Bandung, 2000 3. Gouri, BC., Johnson RA, Statistical Concepts and Methods, John Wiley and Sons, New York, 1977 4. Walpole, RE, ProChapterility and Statistics for Engineer and Scientis, , 2016

Supporting :

1. Draper NR, Smith H., Analisis Regresi Terapan, Gramedia, Jakarta, 1992 2. Spiegel RM, ProChapterility and Statistics, Kin Keong Print, Singapore, 1985

18-21 Mahasiswa mampu determine a simple

linear regression model

• Understanding regression and correlation. • Estimation and testing of Model parameters. • Testing model assumptions.[Ref.1 pp: 300-329, 2 things: 340-361, 6 things: 1-51, 135-169]


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22-24 Final Exam

Course

Course Name : Statistical Methods


Credit : 3

Semester : 3


This course is a basic course that is a prerequisite for taking some further courses in the department of Mathematics. This course deals with basic concepts of statistics, descriptive statistics, random variable distributions, special opportunity distributions, average sampling distributions, hose estimates of parameters, hypothesis tests, and simple linear regression. The introduction of the Minitab program is done as a tool to solve simple problems related to data processing and analysis.

Learning Outcome

[C2]




1. Students are able to understand simple statistical problems, analyze with statistical basic methods, and solve them.

2. Students are able to identify data, analyze it using appropriate basic statistical methods, present it orally and written in academic way.

3. Students are able to be responsible for the conclusions drawn based on data and methods which have learnt during the course.

Main Subject

Basic concepts of statistics, descriptive statistics, random variable distribution, special opportunity distributions, average sampling distributions, hose estimates of parameters, hypothesis testing, and simple linear regression

Prerequisites

Mathematics II

Reference

1. Walpole, R.E, Pengantar statistika, edisi 3, Gramedia, Jakarta, 2002 2. Walpole, R.E, Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan,

edisi 3, ITB, Bandung, 2000 3. Gouri, BC., Johnson RA, Statistical Concepts and Methods, John Wiley

and Sons, New York, 1977 4. Walpole, RE, Probability and Statistics for Engineer and Scientis, , 2016


1. Draper NR, Smith H., Analisis Regresi Terapan, Gramedia, Jakarta, 1992 2. Spiegel RM, Probability and Statistics, Kin Keong Print, Singapore, 1985

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