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COLLEGE OF SCIENCE AND TECHNOLOGY COURSE SYLLABUS

MTH 107 College Algebra 3(3-0) Desig No. Title Credit/Mode I. Bulletin Description:

Complex numbers, introduction to functions, zeros, graphing, linear functions, quadratic functions, intersections of graphs, interpreting graphs, inequalities, polynomial and rational functions, algebra of functions. Course does not count toward a major minor in mathematics except for students pursuing a B.S. in Ed., Elementary Education.

II. Prerequisites: Successful completion of MTH 105 or equivalent competency. III. Rationale for Course Level: College Algebra is an entry level course which historically has been considered a freshman course level. IV. Textbooks and Other Materials to be Furnished by the Student: David Cohen, College Algebra, 3rd ed., West Publishing Company. V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Lecture, discussion, and teacher-directed activities. VII. Course Objectives: After completion of College Algebra the student will be able to: 1. Use real and complex numbers to solve systems of equations, inequalities; find zeros for polynomial functions, rational functions, and logarithmic functions. 2. Use the rectangular coordinate system to graph lines, polynomial functions, rational functions, exponential functions, logarithmic functions and conics centered at the origin. 3. Use college algebra in some applications of mathematics.

VIII. Course Outline: i. Fundamental Concepts A. Real Numbers (1 week) 1. Properties of real numbers 2. Absolute value 3. Integer exponents and scientific notation 4. Rational Exponents B. Polynomials (1/2 week) 1. Polynomials and factoring 2. Rational (fractional) expressions C. Complex Numbers (1/2 week) 1. Definition 2. Arithmetic *3. Graphing

ii. Equations and Inequalities (2 weeks) A. Linear equations B. Quadratic equations C. Applications D. Quadratic type equations E. Linear inequalities F. Quadratic-rational inequalities

iii. Graphs and Lines (2 weeks) A. Rectangular coordinates, distance, midpoint B. Graphs and symmetry C. Equations of lines 1. slope 2. point slope 3. slope intercept 4. general equation D. Parallel and perpendicular lines

iv. Functions (2 weeks) A. Definition B. Graph of a function C. Graphing techniques and special functions D. Algebra of function 1. addition-subtraction, multiplication-division 2. composition E. Inverse functions

*F. Variation

v. Polynomial and Rational Functions (2 weeks)

A. Linear function B. Quadratic functions C. Applications *D. Max-min applications E. More general polynomial functions F. Graphs of rational functions

vi. Exponential and Logarithmic Functions (2 weeks) A. Exponential functions B. Natural base exponential functions C. Logarithmic functions D. Properties of logarithms *E. Applications

vii. Systems of Equations (1 week) A. Linear systems of equations *B. Nonlinear systems of equations

viii. Roots of Polynomial Equations (1 week) A. Synthetic division B. Factor and remainder theorems *C. Fundamental Theorem of Algebra *D. Rational and irrational roots 1. Rational root theorem 2. Upper lower bounds test 3. Location tests *E. Conjugate roots

ix. Conic Sections (1 week) A. Parabola

B. Ellipse C. Hyperbola * optional units, individual teacher's choice, nice to do if schedule permits but not essential. This course syllabus has some overlap with MTH 105. This was done because many of the students will come directly from high school with a variety of equivalents (to MTH 105), but different backgrounds. Because of the variety of backgrounds of our students, a number of topics are listed as optional. It is the responsibility of the teacher to be well-

planned and maintain a brisk pace, yet not overwhelm serious college algebra students. Many of these students need to sharpen their basic algebra skills.

IX. Evaluation: Two or three one-hour exams Quizzes, homework, and cooperative Group work Comprehensive final examination % used for final grade - instructor option X Bibliography:

Fleming, Varberg and Kasube, College Algebra: A Problem Solving Approach, 4th ed., Prentice Hall, 1992.

Grossman, College Algebra, 2nd ed., Saunders College Publishing, 1992.

Hall, College Algebra with Applications, 3rd ed., PWS-Kent, 1992.

Hungerford and Mercer, College Algebra, 2nd ed., Saunders College Publishing

1991.

Kelly, Anderson, and Balomenos, College Algebra, 2nd ed., Houghton Mifflin Company, 1992.

Munem and Foulis, College Algebra with Applications, 3rd ed., Worth Publishers, 1992.

Syllabus prepared by: Dr. William Miller _________________________________ Signature October 19, 1998

CENTRAL MICHIGAN UNIVERSITY COLLEGE OF SCIENCE AND TECHNOLOGY

COURSE SYLLABUS MTH 132 ____Calculus I_____ 4(4-0) Desig. No. Title Credit/Mode I. Bulletin Description: Limits, continuity, differentiation of algebraic and trigonometric functions, applications of derivatives, antiderivatives, definite integrals, Fundamental theorem, exponential and logarithmic functions. Credit may not be earned in both MTH 132 and MTH 136. II. Prerequisites: MTH 130, or equivalent. (Group II-B) III. Rationale for Course Level: IV. Textbooks and Other Materials to be Furnished by the Student:

James Stewart, Calculus: Concepts and Contexts, Brooks/Cole Publishing Company, 1998. (Some sections may use a different book. See the course notes in the Course Offering Guide.)

V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Lecture and discussion format. VII. Course Objectives: The basic goal of calculus is to develop an understanding of the universe in terms of the instantaneous rates of change of phenomena. For example, for a moving object, it is concerned with the rate of change of distance with respect to time at a given instant of time - the instantaneous velocity. The rate of change of physiological activity, measured in terms of the rate of consumption of oxygen per second, is a rate of change - the metabolic rate. The rate of change of total revenue of an industry to the number of items sold is a rate of change - the marginal revenue. To sum up: the rate of change of one variable with respect to another is a useful quantity in many situations.

Calculus is composed of differential calculus and integral calculus. MTH 132 is primarily concerned with differential calculus although integration is introduced in the last third of the course. The basic process in differentiation is to start with a relation between two variables and to find the instantaneous rate of change of one variable with respect to the other. With integration the process is reversed: begin with the rate of change of one variable with respect to another and find a relation between the variables. The Fundamental of Calculus ties the two processes together. Mathematics 132 is designed to: 1. Develop an understanding of the basic principles of differential calculus: limits, continuity, derivatives as limits and as measures of rates of change, differentiation techniques, basic theorems including the Mean Value Theorem. 2. Provide an introduction to the basic ideas of integral calculus: definite integrals as limits and as measures of areas, power rule integration and the technique of substitution, the Fundamental Theorem of Calculus. 3. Enable the student to describe events with mathematical models, analyze the model via the calculus, and interpret the results in terms of the event. The models will employ continuous and differentiable functions. 4. Enhance the students ability to reason deductively by analyzing a situation formulating appropriate hypotheses and assumptions and draw pertinent conclusions. VIII. Course Outline: I. Limits and Continuity (3 weeks) II. The Derivative (4 weeks) III. Applications of the Derivative (3 weeks) IV. Integrals (2 weeks) V. Inverse Functions, Logarithmic and Exponential Functions (3 weeks) The tests and quizzes given in Calculus I contain three types of problems: 1. Proofs: Here, students must present a complete, logical argument for the conclusion of the statement to be proved. They must identify their assumptions, and they must justify each step leading to the conclusion

by previously established criteria. 2. Applications of Theory: The students must analyze the information given in the problem. They then must find a mathematical proposition or a

mathematical model whose conditions are satisfied by the given problem. After showing these conditions are satisfied, he or she must interpret the general conclusion of the proposition in terms of the specific data in the problem.

3. Exercises: This type of problem involves the application of some mathematical technique to produce an answer. The first two types of problems require the student to express his thoughts in a

meaningful way. The third type is more computational in nature. IX. Evaluation: Weekly quizzes, three one-hour examinations, final examination. X. Bibliography:

Anton, Howard, Calculus with Analytic Geometry, 4th ed, John Wiley & Sons, Inc., New York, 1992.

Dick, Thomas and Charles Patton, Calculus, PWS-Kent Publishing Company,

Boston, 1992.

Holder, DeFranza and Jay Pasachoff, Single Variable Calculus, 2nd ed, Brooks/Cole Publishing Company, California, 1994.

Hughes-Hallet, Deborah and Andrew Gleason, et.al., Calculus, John Wiley &

Sons, Inc., New York, 1994.

Larson, Hostetler and Bruce Edward, Calculus with Analytic Geometry, 5th ed, D.C. Heath and Company, Lexington, 1994.

Repka, Joe, Calculus with Analytic Geometry, Wm. C. Brown Publishers, Iowa,

1994.

Stewart, James, Calculus, 2nd ed., Brooks/Cole Publishing Company, California, 1991.

Syllabus prepared by: Douglas W. Nance (updated by Thomas J. Miles) November 30, 1995 (March 17, 2000)


COURSE SYLLABUS MTH 133 Calculus II 4(4-0) Desig. No. Title Credit/Mode I. Bulletin Description: Inverse trigonometric and hyperbolic functions, techniques of integration, applications of definite integrals, indeterminate forms, improper integrals, infinite

series, Taylor series, polar coordinates. Credit may not be earned in both MTH 133 and MTH 137.

II. Prerequisites: MTH 132 or MTH 136 III. Rationale for course level (new courses and level changes): IV. Textbooks and other required materials to be furnished by the

student: Swokowski, Olinick and Pence, Calculus, 6th ed., PWS Publishing Company, 1994. V. Special requirements of the course: None. VI. General methodology used in teaching the course: Lecture and discussion VII. Course objectives: Calculus is composed of differential calculus and integral calculus. MTH 133 is primarily concerned with integral calculus. Students will learn several techniques of integration in this course along with applications of integration in finding volumes of solids, arc length, work done by a force etc. Students are also introduced to the ideas of convergence and divergence of infinite series with applications in approximation of functions.

VIII. Course outline: Swokowski, Olinick and Pence, Calculus, 6th ed. I. Inverse trigonometric functions, hyperbolic functions, indeterminate forms and l’Hopital’s rule (6.7-6.9) 2 weeks II. Applications of the definite integral (5.1-5.7) 3 weeks III. Techniques of integration (7.1-7.7) 4 weeks IV. Infinite Series (8.1-8.9) 4 weeks V. Parametric equation and polar coordinates (9.1-9.4) 2 weeks IX. Evaluation: Weekly quizzes, three one-hour examinations, final examination. X. Bibliography: 1. Anton, Howard, Calculus with Analytic Geometry, 4th ed., John Wiley & Sons, New York, 1992. 2. Berkey, Dennis and Blanchard, Paul, Calculus, 3rd ed., Saunders College Publishing, New York, 1992. 3. Ellis, Robert and Gulick, Denny, Calculus with Analytic Geometry, 4th ed., Harcourt, Brace Jovanovich, New York, 1990. 4. Hunt, Richard, Calculus, 2nd ed., Harper-Collins, New York, 1994. 5. Leithold, Louis, The Calculus with Analytic Geometry, 6th ed., Harper & Row, New York, 1990. 6. Stewart, James Calculus, 2nd ed., Brooks/Cole, California, 1991. Syllabus prepared by: Sivaram K. Narayan ______________________________________ Signature October 26, 1995


COURSE SYLLABUS MTH 151 Mathematics for Elementary Teachers I 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description: Mathematical background for elementary teachers. Sets, numeration systems,

operations with natural numbers, rational numbers, elementary number theory. Admission limited to students pursuing a B.S. in Ed., Elementary Emphasis. No Credit in both 151 and 201 except by permission of department chairperson.

II. Prerequisites: One of: MTH 105, 106, 107, 130, 132 III. Rationale for course level (new courses and level changes): Course contains entry level material required for other courses numbered 152

and above. IV. Textbooks and other required materials to be furnished by the

student: Mathematics Activities for Elementary School Teachers: A Problem Solving

Approach By Dolan, Williamson and Muri. The Addison-Wesley Advantage Cuisenaire’s Manipulative Starter Kit.

V. Special requirements of the course: None. VI. General methodology used in teaching the course: Activity sessions, class discussions, problem solving exercises and lectures.

A considerable number of problems to be solved and exercises to be completed. VII. Course objectives: 1. To provide mathematical background for elementary teachers. 2. To study mathematical models used in elementary school mathematics. 3. To help build a positive attitude toward mathematics. 4. To strengthen understanding of the arithmetic algorithms used in elementary

school mathematics programs.

5. To develope understanding of problem solving strategies. 6. To become familiar with manipulatives used to teach mathematics. VIII. Course outline: All of the following topics will be illustrated with appropriate problem solving activities, manipulatives and other models.

I. Problem Solving (Two weeks, continuation throughout the course.) A. Problem solving steps B. Problem solving strategies C. Applications

II. Sets and Logic (One week) A. Set concepts-universal, null, finite, infinite B. Set relationships-equal, equivalent, subset, disjoint C. Operations-Union, intersection D. Logic-sets as used in problem solving activities

III. Numeration and Computation (Four weeks) A. What is a Numeration System 1. Symbols (numerals) and Bases (grouping) 2. Principles- addition, subtraction, multiplication, positional, place

value B. Historical Systems- such as Roman, Egyptian, Mayan, Babylonian C. Hindu-Arabic Numeration System 1. Symbols, base, principles 2. Notation-word-name numerals, expanded, exponential D. Non-decimal Numeration Systems-demonstrated with models 1. Regrouping process, writing numerals 2. Work with bases other than base ten

III. Number and Number Systems (One Week) A. Whole Numbers 1. Operation definition a. Addition b. Subtraction c. Multiplication - grouping, arrays, continued addition d. Division - Inverse operation (find missing factor),

continued subtraction IV. Integers (One Week)

A. Charged particle model B. Absolute value C. Opposite integers D. Integers around us E. Addition and subtraction of integers F. Number line model G. Operations 1. Addition patterns 2. Subtraction patterns

3. Multiplication a. Multiplication patterns 4. Division F. Applications

V. Number Theory (Three Weeks) A. Square numbers B. Sieve of Eratosthenes C. Cuisenaire rods for finding factors and multiples D. GCF and LCM E. Prime and composite numbers 1. Building Prime Factor Trees For Finding GCF and LCM 2. Fundamental theorem of arithmetic F. Divisibility tests for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19 G. Applications

VI. Rational Numbers (One Week) A. Definition of fraction B. Equivalent fractions C. Order relation D. Operations 1. Addition 2. Subtraction 3. Multiplication 4. Division E. Ratios F. Applications

VII. Decimals and Percents (Two Weeks) A. Definition B. Operations and order

1. Multiplication as repeated addition, decimal arrays and fractional

parts C. Percent as part of one hundred 1. from fractions to decimals to percents D. Applications of decimals and percents IX. Evaluation: Hour tests, activity worksheets, and a final examination. Quizzes and homework

may also be utilized in grading. X. Bibliography:

Bennett, Nelson, Mathematics For Elementary Teachers A Conceptual Approach, Wm Brown Publishers, 1992.

Bennett, Nelson, Mathematics For Elementary Teachers an Activity Approach, Wm Brown Publishers, 1992.

Billstein, Libeskind, Lott, A Problem Solving Approach to Mathematics for Elementary School Teachers., Addison-Wesley Publishing Company, 1993.

Garrison, Victoria J., Student Activity Book to accompany Sgroi/Sgroi’s Mathematics For Elementary School Teachers, PWS Publishing

Company, 1993.

Mayberry, Bath, Student Resource Manual to Accompany Mathematics for Elementary Teachers and Interactive Approach, Saunders College Publishing, 1993.

Musser, Burger, Mathematics for Elementary Teachers A Contemporary Approach., Macmillian College Publishing Company, 1994.

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School. The Council, 1989

Sanson, Swenson, Student Resource Handbook Mathematics for Elementary Teachers a Contemporary Approach., Macmillian Publishing Company, 1991.

Sgroi, Sgroi, Mathematics for Elementary School Teachers Problem-Solving Investigations., PWS-KENT Publishing Company, 1993.

Syllabus prepared by: Donna B. Ericksen _____________________________________ Signature April 6, 1995

CENTRAL MICHIGAN UNIVERSITY


MTH 152 Mathematics for Elementary Teachers II 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description: Continuation of MTH 151. Decimals, percent, ration/proportion, geometry

(concepts and measurement), probability, statistics, introduction to algebra. II. Prerequisites: Math 151 and one of: MTH 105, 106, 107, 130, 132. III. Rationale for course level (new courses and level changes): Course contains entry level material required for other courses numbered 200 and

above. IV. Textbooks and other required materials to be furnished by the

student: Mathematics Activities for Elementary School Teachers: A Problem Solving

Approach By Dolan, Williamson and Muri. The Addison-Wesley Advantage... Cuisenaire’s Manipulative Starter Kit.

V. Special requirements of the course: None. VI. General methodology used in teaching the course: Activity sessions, class discussions, problem solving exercises and lectures. A

considerable number of problems to be solved and exercises to be completed. VII. Course objectives: V. To continue the development of mathematical background and attitude begun

in MTH 151. 2. To continue development of problem-solving strategies and manipulative use. 3. To develop understanding of geometric concepts and activities used in

elementary schools. 4. To develop understanding of elementary probability and statistics concepts

and techniques (including graphing techniques). 5. To introduce microcomputing and algebra concepts. VIII. Course outline: All of the following topics will be illustrated with appropriate problem solving activities, manipulatives and other models.

I. Decimals, Percents, Ratios and Proportion (1 week) A. Scientific Notation

B. Operations with Decimals and Percent C. Ratio and Proportion D. Applications

II. Probability (2 weeks) A. Introduction to Probability B. Fair games C. Binomial Probabilities 1. Pascal’s triangle for analysis D. Area Models E. Monte Carlo Simulations F. Applications

III. Exploring Data, Statistics (3 weeks) A. Different averages 1. mean, median, mode B. Descriptive statistics/ graphing 1. Levels of graphing a. object, pictorial, symbolic 2. Line graphs 3. Bar graphs 4. Stem and Leaf plots a. back-to-back stem and leaf plots 5. Box and Whisker plots

a. lower extreme, upper extreme, median, lower quartile, upper quartile, interquartile range, outliers

C. Gathering statistical information D. Applications

IV. Microcomputers (3 weeks) A. Word processing B. The information Super-Highway 1. E-mail C. Graphing capabilities D. Programming E. Applications for teachers

V. Geometry (4 weeks) A. Geometric Concepts 1. angle measures 2. plane figures, polygons a. classifying, relationships B. Measurement/ Perimeter, Area, and Volume 1. Measurement systems 2. Perimeter, area of plane figures 3. Surface area a. nets 4. Volume of Space figures C. Coordinate and Transformational Geometry 1. Coordinate System

2. Refections 3. Translations 4. Rotations

VI. Introduction to Algebra (2 weeks) A. Solving equations and inequalities B. Graphing of equations and inequalities, linear systems C. Functions. IX. Evaluation: Hour tests, activity worksheets, and a final examination. Quizzes and homework may also be utilized in grading. X. Bibliography:

Bennett, Nelson, Mathematics For Elementary Teachers A Conceptual Approach, Wm Brown Publishers, 1992.

Bennett, Nelson, Mathematics For Elementary Teachers an Activity Approach, Wm Brown Publishers, 1992.

Billstein, Libeskind, Lott, A Problem Solving Approach to Mathematics for Elementary School Teachers., Addison-Wesley Publishing Company, 1993.

Garrison, Victoria J., Student Activity Book to accompany Sgroi/Sgroi’s Mathematics For Elementary School Teachers, PWS Publishing Company, 1993.

Mayberry, Bath, Student Resource Manual to Accompany Mathematics for Elementary Teachers and Interactive Approach, Saunders College Publishing, 1993.

Musser, Burger, Mathematics for Elementary Teachers A Contemporary Approach., Macmillian College Publishing Company, 1994.

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School. The Council, 1989

Sanson, Swenson, Student Resource Handbook Mathematics for Elementary Teachers a Contemporary Approach., Macmillian Publishing Company, 1991.

Sgroi, Sgroi, Mathematics for Elementary School Teachers Problem-Solving Investigations., PWS-KENT Publishing Company, 1993.

Syllabus prepared by: Donna B. Ericksen _____________________________________ Signature April 6, 1995


COURSE SYLLABUS MTH 175 Discrete Mathematics 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description: Topics in discrete mathematics including sequences, graphs, mathematical induction, recursion, number theory, combinatorial counting, difference equations, algorithms, and Boolean Algebra. No credit in MTH 175 after credit in MTH 375 or MTH 332. II. Prerequisites: MTH 130 or equivalent. III. Rationale for Course Level: This course contains introductory topics in discrete mathematics which are required for use throughout the computer science and mathematics curriculum. IV. Textbooks and Other Materials to be Furnished by the Student: Susanna S. Epp, Discrete Mathematics with Applications, 2nd ed., PWS, Boston, 1995. V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Lecture and discussion. VII. Course Objectives: Discrete mathematics concerns processes that consist of a sequence of individual steps. An important aim of an introductory discrete mathematics course is to

develop students’ ability to think abstractly. This is achieved, in part, by studying logic and techniques of proof.

A further objective of the course is to teach the students “recursive thinking.” Recurrence relations allow one to solve a problem for a given case, by assuming that the problem has been solved for smaller cases. The solutions to recurrence relations are often verified using mathematical induction - a proof technique

which is powerful and widely used in mathematics. Students also learn combinatorial counting, the ability to count and arrange

objects is needed in many disciplines where mathematics is applied. Students should also gain an understanding of a variety of discrete structures, such as, functions, relations and graphs. Such structures are also widely used in mathematics. The overall objective of this course is that students gain an understanding of many of the discrete mathematics topics that underlie science and technology. VIII. Course Outline: Chapter 1 - The Logic of Compound Statements 1.5 weeks Section 1.1 - Logical Form and Logical Equivalence Section 1.2 - Conditional Statements Section 1.3 - Valid and Invalid Arguments Section 1.4 - Application: Digital Logic Circuits Section 1.5 - Application: Number Systems and Circuits for Addition Chapter 2 - The Logic of Quantified Statements .5 week Section 2.1 - Predicates and Quantified Statements I Chapter 4 - Sequences and Mathematical 1.5 weeks Induction Section 4.1 - Sequences Section 4.2 - Mathematical Induction I Section 4.3 - Mathematical induction II Section 4.4 - Strong Mathematical Induction and the Well-Ordering Principle Chapter 5 - Set Theory 1 week Section 5.1 - Basic Definitions of Set Theory Section 5.3 - The Empty Set, Partitions, Power Sets, and

Boolean Algebras

Chapter 6 - Counting 2.5 weeks Section 6.1 - Counting and Probability Section 6.2 - Possibility Trees and the Multiplication Rule Section 6.3 - Counting Elements of Disjoint Sets: The

Addition Rule Section 6.4 - Counting Subsets of a Set: Combinations Section 6.6 - The Algebra of Combinations Section 6.7 - The Binomial Theorem Chapter 7 - Functions 1 week Section 7.1 - Functions Defined on General Sets Section 7.2 - Application: Finite - State Automata Section 7.3 - One - to - One and Onto, Inverse Functions Chapter 8 - Recursion 1.5 weeks Section 8.1 - Recursively Defined Sequences Section 8.2 - Solving Recurrence Relations by Iteration Section 8.3 - Second-Order Linear Homogeneous Recurrence

Relations with Constant Coefficients Chapter 10 - Relations 1 week Section 10.1 - Relations on Sets Section 10.2 - Reflexivity, Symmetry, and Transitivity Section 10.3 - Equivalence Relations Chapter 11 - Graphs and Trees 3 weeks Section 11.1 - Graphs: An Introduction Section 11.2 - Paths and Circuits Section 11.3 - Matrix Representations of Graphs Section 11.5 - Trees Section 11.6 - Spanning Trees IX. Evaluation: Tests (2, 20% each), final examination (30%), homework and quizzes

(20%), computer projects (10%). X. Bibliography: Bogart, K. P., Introductory Combinatorics, 2nd ed., Harcourt Brace

Jovanovich, Orlando, 1990. Chartrand, G., Introductory Graph Theory, Dover, New York, 1977.

Dossey, J. A., A. D. Otto, L. E. Spence and C. Vanden Eynden, Discrete Mathematics, 2nd ed., Harper Collins, New York, 1993. Grimaldi, R. P., Discrete and Combinatorial Mathematics, 2nd ed., Addison- Wesley, Reading MA, 1989. Hirschfelder, R. and J. Hirschfelder, Introduction to Discrete Mathematics, Brooks/Cole, Pacific Grove, California, 1991. Rosen, K., Discrete Mathematics and Its Applications, 2nd ed., McGraw-Hill,

New York, 1991. Van Lint, J. H. and R. M. Wilson, A Course in Combinatorics, C.U.P.,

Cambridge U.K., 1992. Syllabus prepared by: Kirsten Fleming ____________________________________ Signature November 7, 1995


COURSE SYLLABUS MTH 223 Linear Algebra Matrix Theory 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description:

Systems of linear equations, matrices, determinants, vectors, vector spaces, eigenvalues, linear transformations, applications and numerical methods. Credit may not be earned in both MTH 137 and 223.

II. Prerequisites: MTH 132 or 136 or equivalent. III. Rationale for Course Level: IV. Textbooks and Other Materials to be Furnished by the Student: Edwards, C. H. and Penny David, Elementary Linear Algebra, Prentice Hall, Englewood Cliffs, New Jersey, 1988. V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Lecture, group activities, problem solving. VII. Course Objectives:

A. After completion of this course, the student will be able to do the following computations: 1. Use Gaussian Elimination to : solve a linear system of equations, find

“for what right sides can a system be solved”, invert a matrix, compute a determinant, find an eigenspace, factor a matrix into an L and a U , factor a matrix into elementary matrices, find a range space for a matrix, explain the meaning of an occurrence of 0 = 0 in a reduced echelon form, find bases for null space, row space and column space.

2. Multiply matrices. 3. Compute determinants.

4. Find the polynomial of degree n or less that exactly fits (n + 1) given points.

5. Solve the normal equations to find a polynomial of best fit for a given set of data.

6. Use the Gram-Schmidt Orthogonalization Process to find an orthogonal basis for a space.

7. Find the orthogonal projection of a vector onto a space. 8. Find eigenvalues and eigenvectors for a matrix. 9. Compute powers of a matrix using eigenvalues. 10. For two given vectors compute sum, difference, dot product, vector

product, angle between, projection of one vector onto the other, etc. 11. Find whether a given transformation is a linear transformation. 12. Find the equation of the “image” of a given “input” equation under a

linear transformation.

B. After completion of this course, the student will be able to do the matrix algebra and know the whys for the following topics: 1. Why X = A-1B follows from AX = B when A is invertible. 2. The Sock-Shoe Theorem (AB)-1 = B-1A-1 . 3. Why the L U Decomposition LY = B and UX = Y follow from

AX = B . 4. Why Elementary Matrices help explain the inverse matrix, the LU

Decomposition and the factoring of a transformation matrix into a composite of shears, reflections, and expansions.

5. A is invertible if and only if det A 0 . 6. The Eigenvalue Problem. 7. The matrix transformation T ( X ) = A X is a linear transformation

C. After completion of this course, the student will be familiar with many of

the applications of Linear Algebra and Matrix Theory: 1. “Real” problems that model into a linear system of equations. 2. Data fitting (both exact and least squares best fit). 3. Where do “large” linear systems of equations occur. 4. The common occurrence of “sums of products” in everyday experience

motivates the definition of matrix multiplication. 5. Coding and Cryptography. 6. Any invertible linear transformation in R2 is a composite of expansions

reflections and shears. 7. Eigenvalues and graphs of conics, eigenvalues and population growth

models, eigenvalues and systems of differential equations.

D. To use a variety of Linear Algebra concepts to solve Linear Modeling Problems.

E. To be introduced to several algorithms of linear mathematics and the

present day technology that has been developed for solving linear problems.

F. To create a transition from computationally oriented courses in

mathematics to the more theoretical ones. Definitions, proofs, algebraic reasoning, etc. are brought in when needed.

VIII. Course Outline: A. Systems of Linear Equations [ 2 weeks ]

1. Methods for Solving Linear Systems 2. Gaussian Elimination 3. LU Decomposition 4. Partial Pivoting 5. MeanWhat Right Sides can you Solve 6. Where do Large Systems Occur 7. Homogenous Systems 8. Applications 9. Data Fitting 10. Numerical Methods.

B. Matrices [ 2 weeks ] 1. Matrix Addition 2. Matrix Multiplication 3. Matrix Algebra 4. Linear systems in Matrix Notation 5. Identity Matrix 6. Inverses 7. Elementary Matrices 8. Transpose 9. Applications

C. Determinants [ 2 weeks ] 1. Calculation of Determinants 2. Minors, Cofactors 3. Properties of Determinants 4. Cofactor Matrix, Adjoint Matrix 5. Inverse of a Matrix using Cofactors 6. A is invertible if and only if det A0 7. Cramer’s Rule 8. Vandermonde Determinant 9. Determinants and Data Fitting

D. Vectors [ 2 weeks ] 1. Addition of Vectors, Scalar Multiplication 2. Length of a Vector 3. Dot Product of Vectors and Angle 4. Cross Product 5. Lines 6. Planes

E. Vector Spaces [ 2 weeks ]

1. The Vector Spaces R2, R3 and Rn 2. Subspaces 3. Linear Combinations 4. Span 5. Linear Dependance and Independence 6. Basis 7. Dimension 8. Orthogonal Basis 9. Orthogonal Projection onto a Space 10. Null Space 11. Column (Range ) Space 12. Row Space

F. Least Squares [ 1 week ] 1. Polynomial Least Squares Data Fitting 2. Normal Equations 3. Orthogonal Projection onto a Range Space

G. Eigenvalues [ 2 weeks ] 1. The Eigenvalue Problem 2. Finding Eigenvalues and Eigenvectors 3. Diagonalization 4. Powers of a Matrix by Eigenvalues 5. Symmetric Matrices and Orthogonal Eigenvectors 6. Population Models

H. Linear Transformations [ 2 weeks ] 1. Definition and Examples 2. Matrix Transformations T ( X ) = A X 3. Geometric Transformations of R2 4. All Linear Transformations from Rn to Rm are of the form

T ( X ) = A X for some matrix A 5. Elementary Properties 6. Range 7. Kernel 8. Rank 9. Isometries, Rotations, Computer Graphics

IX. Evaluation: Exams, final exam and quizzes or homework or class presentations.

Frequency and type determined by the instructor. An estimate of the grading weights for these evaluation methods would be 50% semester exams, 30% final exam, 20% quizzes or homework or class presentations.

X. Bibliography:

1. Anton, Howard, and Chris Rorres. Elementary Linear Algebra, 6th ed. New York: John Wiley and Sons, Inc., 1991.

2. Edwards, C.H., and David Penny. Elementary Linear Algebra. Englewood

Cliffs, New Jersey: Prentice Hall, 1988. 3. Fraleigh, John and Raymond Beauregard. Linear Algebra. Reading,

Massachusetts: Addison Wesley, 1987. 4. Goldberg, Jack. Matrix Theory with Applications. New York: McGraw Hill,

1991. 5. Hill, Richard. Elementary Linear Algebra with Applications, 2nd ed.

Harcourt, Brace, Jovanovich, 1991. 6. Johnson, Riess and Arnold. Linear Algebra, 3rd ed. Reading, Massachusetts:

Addison Wesley, 1993. 7. Kolman, Bernard, 8. Leon, Steven. Linear Algebra with Applications, 3rd ed. New York:

Macmillan, 1990. 9. Lay, David. Linear Algebra and its Applications. Reading, Massachusetts:

Addison Wesley, 1994. 10. Schneider, Dennis. Linear Algebra, A Concrete Introduction. New York:

Macmillan, 1987. 11. Strang, Gilbert. Linear Algebra and its Applications, 3rd ed. Harcourt, Brace,

Jovanovich, 1988. 12. Strang, Gilbert. Introduction to Linear Algebra. Wellesley, Massachusetts :

Wellesley-Cambridge Press, 1993. 13. Tucker, Alan. Linear Algebra. New York: Macmillan, 1993. 14. Williams, Gareth. Linear Algebra with Applications, 2nd ed.Dubuque, Iowa:

Wm. C. Brown Publishers, 1991. Syllabus prepared by: Arnold Hammel ___________________________________ Signature ___________________________________ Date


COURSE SYLLABUS MTH 233 _____Calculus III_____ 4(4-0) Desig. No. Title Credit/Mode V. Bulletin Description:

Vectors and surfaces in R3, vector-valued functions, functions of several variables, partial differentiation and some applications, multiple integrals, vector calculus.

II. Prerequisites: MTH 137 or both MTH 133 and MTH 223. III. Rationale for Course Level: The course has a 200 level prerequisite. IV. Textbooks and Other Materials to be Furnished by the Student:

Swokowski, Olinick and Pence: Calculus, 6th ed., PWS Publishing Company, 1994

V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Lecture, discussion and problem solving. VII. Course Objectives:

Students will learn basic concepts of multivariable calculus with emphasis on functions of two and three variables. Students will become familiar with partial differentiation, multiple integration, line and surface integrals along with their applications in science and engineering problems. Students will use linear algebra to aid their understanding of multivariable differentiation and integration.

VIII. Course Outline: Swokowski, Olinick and Pence: Calculus, 6th ed. 1. Vectors and surfaces (10.1-10.6). [2 weeks] 2. Vector-valued functions (11.1-11.5) [2 weeks] 3. Partial differentiation (12.1-12.9) [4 weeks] 4. Multiple integrals (13.1-13.8) [4 weeks] 5. Vector calculus (14.1-14.7) [3 weeks] IX. Evaluation: Quizzes/homeworks, three one-hour examinations, final examination. X. Bibliography: VI. Anton, Howard: Calculus with Analytic Geometry, 4th ed., John Wiley &

Sons, New York, 1992. 2, Berkey, Dennis and Blanchard, Paul, Calculus, 3rd ed., Saunders College Publishing, New York, 1992. 3. Ellis, Robert and Gulick, Denny, Calculus with Analytic Geometry, 4th ed., Harcourt, Brace Jovanovich, New York, 1990. 5. Hunt, Richard, Calculus, 2nd ed., Harper-Collins, New York, 1994. 6. Larson, Hostetler and Edwards: Calculus with Analytic Geometry, 5th ed., D.C. Heath & Company, Lexington, MA 1994. 7. Leithold, Louis, The Calculus with Analytic Geometry, 6th ed., Harper & Row, New York, 1990. 8. Marsden , Jerrold and Tromba, Anthony, Vector Calculus, 3rd ed., W.H.

Freeman and Co., New York, 1988. 8. Steward, James, Calculus, 2nd ed., Brooks/Cole, California, 1991. Syllabus prepared by: ____Sivaram K. Narayan_______________ Name ___________________________________ Signature ___________________________________ Date


COURSE SYLLABUS MTH 251 Geometry for Elementry Teachers 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description:

Geometrical concepts such as parallelograms, triangles, circles, spheres, volume, and area. Admission limited to students pursuing a B.S. in Ed., Elementary Emphasis. May not be counted toward major, minor in mathematics except on Elementary Education Curriculum.

II. Prerequisites: MTH 151 and MTH 152. III. Rationale for Course Level:

. IV. Textbooks and Other Materials to be Furnished by the Student: Geometry in the Middle Grades, Addenda Series, Dorothy Geddes, NCTM, 1992.

Geometry: An Investigative Approach, 2nd ed., Phares O’Daffer, Stanley Clemens and Bryce Thinquist, Addison Wesley, 1992.

V. Special Requirements of the Course: Assignments and reports using materials in Science and Math Teaching Center, IMC, & Park Library

VI. General Methodology Used in Conducting the Course:

Lab activities (in small groups), discussions, lecture. VII. Course Objectives: VI. To provide the prospective elementary teacher with a background of fundamental

geometric concepts. VII. To help the student develop intuitive approaches to understanding of geometric

concepts. VIII. To study how children learn geometric concepts. IX. To demonstrate some procedures for teaching geometric concepts to children. VIII. Course Outline:

VII. Overview of Geometry (4 hours) 9. Environmental 10. As a ,mathematical system 11. An art

VIII. How Children Learn Geometric Concepts (2 hours) IX. Intuitive Geometry

Geometric concepts demonstrated and taught by discovery by using paperfolding, geoboards, miras, mirrors, etc.

b. Points and Lines (1 hour) c. Angles (2 hours) d. Polygons (12 hours)

A. Triangles B. Quadrilaterals C. N-gons D. Regular Polygons E. Star Polygons F. Theorems About Polygons G. Symmetry H. Tesselations

1) Regular 2) Semi-Regular 3) Dual

e. Circles (2 hours): Perimeter (developing formula) f. Polyhedron (5 hours): Area (developing formula)

A. Construction, Nets B. Prisms, Pyramids C. Regular, Platonic D. Deltahedra E. Semiregular F. Symmetry in Space

g. Motion Geometry (4 hours) G. Translations (slide) H. Reflections (flips) I. Rotation (turns) J. Combinations of 1, 2, & 3 K. Motion Geometry with Coordinates

h. Congruence (1 hour) i. Measurements (6 hours)

13. Process – precision and accuracy-systems: metric, English 14. Length, Area, Volume 15. Angle

IX. Evaluation: Quizzes, 3 or 4 exams, projects and reports X. Bibliography:

8. Bennett, A.B. & Nelson, L.T. Mathematics: An Activity Approach, 2nd edition, Allyn & Bacon, 1985.

9. Dolan, D., Williamson, J. & Muri, M., Mathematics Activities for Teachers: A Problem Solving Approach, 2nd edition, Addison-Wesley, 1993.

10. Geltner, P. & Peterson, D., Geometry for College Students, 3rd edition, PWS Publishing, 1995.

11. Hirsch, C., Motion in Geometry, MCTM, Monograph #10, 1976. 12. Miller, W., Geometry Laboratory Activities I, J. Weston Walch, 1975. 13. NCTM, Curriculum & Evaluation Standards for School Mathematics,

1989. 14. NCTM, Geometry in the Mathematics Curriculum, 36th Yearbook, 1973. 15. Sobel, J. & Maletsky, M., Teaching Mathematics: A Sourcebook of Aids,

Activities & Strategies, 2nd edition, Prentice Hall, 1988. 16. Swanson, J. and Swenson, K., Student Resource Handbook, Mathematics

for Elementary Teachers, A Contemporary Approach, 2nd edition, MacMillan, 1991.

17. Wenninger, M., Polyhedron Models for the Classroom, NCTM, 1966. Syllabus prepared by: ___________Martha L. Frank_____________

_____________________________________ Signature

_____________________________________ Date


COURSE SYLLABUS MTH 253 History of Elementary Mathematics 2(2-0) Desig. No. Title Credit/Mode I. Bulletin Description:

History of numeral systems, computational algorithms and devices, time, number theory, calendar, and geometry. Admission limited to students pursuing a B.S. in Ed., Elementary Emphasis. Credit cannot be earned in both 253 and 573.

II. Prerequisites: MTH 151 and MTH 152. III. Rationale for Course Level: Content appropriate for sophomores. IV. Textbooks and Other Materials to be Furnished by the Student:

Instructor developed course pack of reprints and notes.

V. Special Requirements of the Course: Written and oral reports on historical topics required. VI. General Methodology Used in Conducting the Course:

Lectures, student reports on primary and secondary sources. VII. Course Objectives: X. The student will gain a basic knowledge of the history of whole number

numeration and computation, as well as other areas of mathematics taught in grades K-8.

XI. The student will learn activities and content that can enrich the elementary classroom teaching of mathematics.

X. Course Outline:

I. Numeral Systems (approximate time – 3 weeks) Primitive, Babylonian, Egyptian systems, Chinese-Japanese traditional, Chinese rod, Greek systems, Roman, Hindu-Arabic, Mayan

II. Computational Devices (approximate time – 3 weeks) Counting Board, Abacus, Napier Rods III. Written Computational Forms (approximate time – 4 weeks) Babylonian methods, Egyptian methods, Hindu-Arabic methods, Erasure, Scratch, Other whole number fraction and decimal methods

IV. Miscellaneous Units (selected by vote of class) (approximate time–5weeks)

Coverage depends upon time available Geometry (Euclid, polygon and polyhedron construction, Golden Rectangle, Dissections, Including Pythagorean theorem) Magic Squares, Time and Calendars, Number Theory, History, Measurement Systems

XI. Evaluation: Three exams are given. Written reports are evaluated.

X. Bibliography: Beckman, Petr, A History of___, St. Martin’s Press, 1971

Burton, David M., The History of Mathematics: An Introduction, 3rd Edition, Allyn and Bacon, 1995. Fauvel, John and Jeremy Gray (eds), The History of Mathematics: A Reader, Macmillan Flegg, Graham (ed), Numbers Through the Ages, Macmillan, 1989. Grinstein, Louise S., and Paul J. Campbell, Women of Mathematics: A Biobibliographic Sourcebook, Greenwood Press, 1987. Ifrah, Georges, From One to Zero: A Universal History of Numbers, Penguin, 1987, (orig. 1981). Katz, Victor, A History of Mathematics, Harper Collins, 1993. Phillips, Esther R., Studies in the History of Mathematics, Mathematical Association of America, 1987. Shirley, John W., Thomas Hariot: A Biography, Oxford, 1983. Stillwell, John, Mathematics and Its History, Springer, 1989. Swetz, F.J., From Five Fingers to Infinity, Open Court, 1994.

Syllabus prepared by: _James K. Bidwell_____________________ Name

_____________________________________ Signature

_____________________________________ Date

Central Michigan University College of Science and Technology

Course Syllabus MTH 332 Introduction to Analysis 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description: Study of several basic concepts in mathematics including logic, set theory, relations and functions, cardinality, number systems sequences. II. Prerequisites: MTH 137 or 223. III. Rationale for course Level This course follows the calculus sequence (100-200 level) and precedes more advanced courses. IV. Textbooks and Other Materials to be Furnished by the Student:

Smith, Eggen and St, Andre, Intermediate Analysis: An Introduction to Mathematical Thought. 4th edition, Brooks/Cole.

V. Special Requirements of the Course: None. VI. General Methodology Used in conducting the Course: Lecture, discussion, group work, and student presentations. VII. Course Objectives:

The objectives of this course are to have the students learn how to think and write mathematically, to accumulate a solid foundation in the materials (sets, relations, functions, and cardinality) needed for advanced courses, and to have the opportunity to explore at some depth one or more of the primary areas of pure mathematics; to make the student aware of the mathematical foundations of subjects taught informally at the secondary and collegiate levels.

VIII. Course Outline: Logic and Proofs: 3 weeks Propositions and connectives, conditionals, quantifiers, rules of inference, proof. Set Theory 3 weeks Operations and extended operations, indexed families of sets, induction Relations: 3 weeks Equivalence relations, congruence module m Functions: 3 weeks composition, inverses, one to one and onto, induced set functions

Cardinality: 3 weeks Finite and infinite sets, countable sets, countability of the rationals, uncountability of the reals, comparability and ordering. Other topics may be selected by the instructor and vary from semester to semester. The intention is to introduce the subject matter of one or more of the principle areas of the study of pure mathematics. The alternatives are:\ Sequences of Real Numbers: Upper and lower bounds, suprema and infina, completeness, convergent sequences, the arithmetic of sequences, Cauchy sequences, subsequences. Concepts of Algebra:

Binary operations, commutativity, associativity, identity and inverses, operation preserving maps, groups, elementary properties of groups, subgroups and quotient groups,

Topological Properties of Reals: Continuous functions, neighborhoods, open sets closed sets, compactness.

IX. Evaluation: By examinations (2-4 per semester), grading hand-in problems, and quizes. X. Bibliography:

1. D’Angelo, John P. and West, Douglas B., Mathematical Thinking: Problem Solving and Proofs, Prentice Hall, 1997.

2. Eisenberg, Murray, The Mathematical Method, Printice Hall, 1996. 3. Enderton, Herbert B., Elements of Set Theory, Academic Press, 1977. 4. Foules, David and Munem, Mustafa A., After Calculus: Algebra, Macmillan, 1988. 5. Galovich, Steven, Doing Mathematics: An Introduction to Proofs and Problem Solving, Saunders College Publishing, 1993. 6. Gordon and Hindman, Elementary Set Theory: Proof Techniques, Hafner

Press, 1975. 7. Kaplansky, Irving Set Theory and Metric Spaces, Allyn and Bacon, 1972. 8. Morash, Ronald P., Bridge to Abstract Mathematics: Mathematical Proof

and Structures, Random House, 1987. 9. Schumacher, Carol, Chapter Zero: Fundamental Notions of Abstract

Mathematics, Addison-Wesley, 1996. 10. Smith, Douglas, Eggen, Maurice, and St, Andre, Richard, A Transition to

Advanced Mathematics, 4th Edition, Brooks/Cole, 1997. Syllabus prepared by ________________________________ Name ________________________________ Signature ________________________________ Date



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COURSE SYLLABUS

MTH 361 Field Experience in Teaching Mathematics 1 (Spec Desig. No. Title Credit/Mode I. Bulletin Description:

Preparation for an experience in working with students in secondary (7-12) mathematics classrooms.

II. Prerequisites: MTH 223 III. Rationale for Course Level: This course is required for junior secondary education mathematics majors. IV. Textbooks and Other Materials to be Furnished by the Student: None. V. Special Requirements of the Course: Participation in secondary classroom activities. VI. General Methodology Used in Conducting the Course: See Outline. VII. Course Objectives: To provide experience in a school setting for secondary mathematics majors at the

junior level. The course should meet the NCATE requirements for a “Mid-tier” experience. The course objectives of preparing students to become mathematics teachers are consistent with the CLEAR’s outcome domains: Concept-and Knowledge-Driven [C], LEArner Centered [LEA], and Reflective Practice Relevant to Diverse Settings and Roles [R]. These objectives function as guides to instruction for enabling candidates to demonstrate the expected outcomes of the CLEAR Conceptual Framework

VIII. Course Outline:

1. Initial meetings (1-3) to orient students and prepare materials appropriate for the subject and student involved.

2. 30-50 hours of secondary classroom experience including paper grading, helping students individually, small group instruction, preparing bulletin boards, etc. At least 50% of the time will be in direct contact with high school students.

3. Final meeting to discuss and evaluate classroom experiences.

Students will be placed in a secondary classroom by the Director of Teacher Education.

IX. Evaluation: Tangible student work ( e.g., bulletin boards and displays) will be evaluated. A

paper, journal, or other report may be required and evaluated. Interaction with secondary students will be observed and evaluated. Each student will be evaluated at least three times.

X. Bibliography:

Barnett, R.A., Teacher Education: A Changing Model of Professional Preparation, Education Studies, 13, 57-74, 1987.

Borich, Gary D., Observation Skills for Effective Teaching, Columbus, OH,

Merrill, 1999. Clark, D.L., Field Experience in Teacher Education, Columbus, OH, National

Center for Research in Vocational Education, 1985. Michigan State Board of Education, Michigan Essential Goals and Objectives for

Mathematics Education, Michigan State Board of Education, 1998. Michigan State Board of Education, An Interpretation of Michigan Essential

Goals and Objectives for Mathematics Education, Michigan State Board of Education, 1998.

Morris, J.E. et al, Standards for Professional Laboratory and Field Experiences:

Review and Recommendations, Action in Teacher Education, 7, 73-78, 1985.

National Council of Accreditation of Teacher Education, Standards, Procedures

and Policies of the Accreditation of Professional Educational Units, Washington, D.C., NCATE, 1987.

National Council of Teachers of Mathematics, Curriculum and Evaluation

Standards for School Mathematics, Reston, VA: NCTM, 1989.

Syllabus prepared by: Charles B. VonderEmbse Name Signature February 1, 1999 Date



MTH 375 Discrete Mathematics 3(3-0) Desig No. Title Credit/Mode

I. Bulletin Description: Relation between set theoretic operations and computer operations, applications, of graph theory, graphical algorithms, discrete algebraic structure.

II. Prerequisites: MTH 133 or 137 or 223; MTH 175 or consent of instructor; and a knowledge of a programming language. III. Rationale for Course Level: This is the second course in Discrete Mathematics. The mathematical maturity required demands that this be a junior-senior level course. IV. Textbooks and Other Materials to be Furnished by the Student:

Introductory Combinatorics, 2nd ed., R.A. Brualdi, North Holland.

V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Dialogue, lecture, homework assignments for classroom discussion. VII. Course Objectives:

To introduce students in computer science and mathematics to discrete mathematical structures and their applications to real life problems.

VIII. Course Outline: 1. Pigeonhole Principle 1 week 2. Permutations and Combinations 2.5 weeks 3. The Binomial Coefficients 2.5 weeks

4. Inclusion – Exclusion Principle 1.5 weeks 5. Eulerian Walks and the Idea of Graphs 1 week 6. Trees 1 week 7. Minimum Cost Spanning Trees 1 week 8. Graphs and Matrices 1 week 9. Network Flows 2 weeks IX. Evaluation: Quizzes, two or three one-hour examinations, and a final exam. X. Bibliography:

Bogart, Introductory Combinatrics, 2nd ed., Harcourt Brace Jovanovich, 1990. Dossey, Otto, Spence, Vanden Eynden, Discrete mathematics, 2nd ed., Harper Collins, 1993. Grimaldi, Discrete and Combinatorial Mathematics, 3rd ed., Addison Wesley, 1994. Kolman, Busby, Ross, Discrete Mathematical Structure, 3rd ed., Prentice Hall, 1995. Merris, Combinatorics, PWS, Publishing Company, 1995.

Syllabus prepared by: ___________________________________________ Name ___________________________________________ Signature ___________________________________________ Date


COURSE SYLLABUS

MTH 461 Teaching of Secondary School Mathematics 4(4-0) D Desig. No. Title Credit/Mode I. Bulletin Description:

Materials, teaching techniques for prospective secondary mathematics teachers. Course does not count as one of the two 400 or 500 level courses on mathematics major. May not be counted toward a major or minor in mathematics except for students pursuing a B.S. in Ed. Degree. Open only to seniors and approved juniors.

II. Prerequisites: MTH 223 or 137, 341. III. Rationale for Course Level: Course is intended to prepare prospective secondary school teachers for the

classroom after they have taken most of their mathematics content courses. IV. Textbooks and Other Materials to be Furnished by the Student:

Johnson, David R. (1982), Every Minute Counts: Making Your Math Class Work, Dale Seymour Publ.

National Council of Teachers of Mathematics (1989), Curriculum and Evaluation Standards for Mathematics, NCTM.

Posamentier, Alfred S. & Stepelman, Jay (1989), Teaching Secondary School Mathematics: Techniques and Enrichment Units, Charles E. Merrill Publishing.

V. Special Requirements of the Course: Out-of-class tutoring for MTH 055-105 VI. General Methodology Used in Conducting the Course: Lectures, discussions, student presentations and cooperative learning. VII. Course Objectives:

1. Students will be aware of the issues and history which shape the current state of mathematics education in secondary schools.

2. Students will examine in depth the current climate of secondary mathematics education, including recent national and international assessments, curricular movements, technological advances, educational research, and successful classroom practices.

3. Students will become prepared for the real world of teaching secondary mathematics through the study and practice of classroom management

techniques, course and lesson preparation, and assessment and evaluation of students, themselves, and curricular programs.

4. Students will become aware of and sensitive to equity and cultural diversity issues in the classrooms and in the school setting.

5. Students will learn to read and use current professional literature and other materials to improve their mathematical skill and concepts and their teaching skills.

6. Students will become true professional mathematics educators by participating in professional organizations, through continued inserve training, and by upgrading their skills in both mathematics and the art of teaching mathematics.

7. Students will be introduced to the use of graphing calculator technology for teaching secondary mathematics.

8. Students will present micro teaching lessons on the topics common to secondary school mathematics.

9. Students will participate in an organized tutoring experience. The course objectives of preparing students to become mathematics teachers are consistent with the CLEAR’s outcome domains: Concept-and Knowledge-Driven [C], LEArner Centered [LEA], and Reflective Practice Relevant to Diverse Settings and Roles [R]. These objectives function as guides to instruction for enabling candidates to demonstrate the expected outcomes of the CLEAR Conceptual Framework

VIII. Course Outline: A. Review of Past and Current State of Mathematics Education (interspersed

throughout the semester). 1. Brief history of Mathematics Education issues and trends during

the 20th century. 2. Current issues in Mathematics Education.

B. Practical Issues of Teaching Mathematics in the Secondary School ( 8 weeks).

This includes concept coordinated activities, significance of sequenced examples, techniques and issues for remediation, use of manipulatives, planning, assessment, enrichment and curriculum development and overview.

C. Examination of teaching methods, including the visual approach, the use of manipulatives, cooperative learning groups, and problem solving strategies. (3 weeks)

D. Using Technology to Teach Mathematics in the Secondary Classroom (interspersed throughout the semester).

E. Microteaching Lessons (3 weeks). F. Tutoring

IX. Evaluation: The instructor will grade assignments, papers, projects, and/or tests as

administered. X. Bibliography:

Aichele, Douglas B. and Coxford, Arthur F. (1994), Professional Development for Teachers of Mathematics: 1994 Yearbook, Reston, Virginia, National Council of Teachers of Mathematics.

Cangelori, James S. (1996), Teaching Mathematics in Secondary and Middle School: An Interactive Approach, 2nd edition, Merrill/Prentice Hall, Columbus, Ohio, 1996.

Coxford, Arthur F. and House, Peggy A. (1995) Connecting Mathematics Across the Curriculum: 1995 Yearbook, Reston, Virginia, National Council of Teachers of Mathematics.

Coxford, A.F. & Shullte, A.P. (eds.) (1988), The Ideas of Algebra K-12: 1988 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Coxford, Arthur R. and Webb, Norman W. (1993), Assessment in the Mathematics Classroom: 1993 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Dossey, John A., et al. (1988), The Mathematics Report Card: Are We Measuring Up?, Educational Testing Service, Princeton, New Jersey, 1988.

Driscoll, Mark (1983), Research Within Reach: Secondary School of Mathematics, Reston, Virginia: National Council of Teachers of Mathematics.

Eckert, P., Kitchen, G., Nichols, C., & VonderEmbse, C. (1989), Graphing Calculators in the Secondary Mathematics Classroom, Monograph #21, Lansing, MI: Michigan Council of Teachers of Mathematics.

Hansen, V.P. & Zweng, M.J. (eds.) (1984), Computers in Mathematics Education: 1984 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Hirsch, Christian R. & Zwent, Marilyn J. (Eds.) (1985), The Secondary School Mathematics Curriculum: 1985 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Johnson, David R. (1982), Every Minute Counts: Making Your Math Class Work, Palo Alto, California: Dale Seymour Publications.

Krulik, Stephen & Reys, Robert E. (Eds.), (1980), Problem Solving in School Mathematics: 1980 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Lindquist, Mary M. & Shulte, Albert P. (Eds.) (1987), Learning and Teaching Geometry, K-12: 1987 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Maletsky, E. and Sobel, M. (1988), Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies, Englewood, NJ: Prentice Hall Publishing Co.

McKnight, Curtis C., et al. (1987), The Underachieving Curriculum: Assessing U.S. School Mathematics from an International Perspective, Champaign, Illinois: Stipes Publishing Company.

National Council of Teachers of Mathematics (1980), An Agenda for Action: Recommendations for School Mathematics for the 1980’s, Reston, Virginia: NCTM.

National Council of Teachers of Mathematics (1995), Addenda Series, Reston, Virginia: NCTM, 1995.

National Council of Teachers of Mathematics (1994), Assessment Standards for School Mathematics, Reston, Virginia: NCTM.

National Council of Teachers of Mathematics (1989), Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia: NCTM.

National Council of Teachers of Mathematics (1991), Professional Standards for Teaching Mathematics, Reston, Virginia: NCTM.

National Council of Teachers of Mathematics, Arithmetic Teacher, Current and back issues.

National Council of Teachers of Mathematics, Mathematics Teacher, Current and back issues.

National Council of Teachers of Mathematics, Journal for Research in Mathematics Education, Current and back issues.

National Research Council (1989), Everybody Counts: A Report to the Nation on the Future of Mathematics Education, Washington, D.C., National Academy Press, 1989.

National Research Council (1990), Reshaping School Mathematics, Washington D.C.: National Academy Press.

Posamentier, Alfred S., & Stepelman, Jay (1989), Teaching Secondary School Mathematics: Techniques and Enrichment Units, Columbus, Ohio: Charles E. Merrill Publishing Company.

Rombert, Thomas A. (1984), School Mathematics: Options for the 1990’s, (Contract No. 400-83-0058), Washington, D.C.: U.S. Department of Education.

Schoen, Harold L. & Zweng, Marilyn J., (Eds.),(1986), Estimation and Mental Computation: 1986 Yearbook, Reston, Virginia: National Council of Teachers of Mathematics.

Suydam, Marilyn N., et al. (Eds.), (1985), Alternative Courses for Secondary School Mathematics, Reston, Virginia: National Council of Teachers of Mathematics.

Syllabus prepared by: Douglas W. Nance Name Signature February 3, 1999 Date



MTH 523 Modern Algebra 3(3-0) Desig. No. Title Credit/Mode 3(3,0)

I. Bulletin Description: Groups, rings, integral domains, fields, and fundamental homomorphism theorems.

II. Prerequisites: MTH 332 or Graduate Status III. Rationale for Course Level: This class is traditionally taught at the senior and/or

graduate level. IV. Textbooks and Other Materials to be Furnished by the Student:

Joseph A. Gallian, Contemporary Abstract Algebra 3rd ed., D.C. Heath and Co., 1993.

V. Special Requirements of the Course: None VI. General Methodology Used in Conducting the Course: Lectures, discussions, and problem solving. VII. Course Objectives:

(1) Introduce the fundamentals of abstract algebra. (2) To strengthen the student's reasoning skills and ability to deal with abstract

mathematics, with an emphasis on problem-solving and proof writing. VIII. Course Outline: I. Groups (about 20 lectures) A. Definition and examples B. Simple properties C. Subgroups D. Cyclic groups E. Permutation groups F. Cosets G. Lagrange's Theorem H. Quotient groups I. Homomorphism and isomorphisms

J. Cayley's Theorem II. Rings, integral domains, and fields (about 20 lectures) A. Definitions, examples, and simple properties B. Subrings and ideals C. Homomorphisms and isomorphisms D. Quotient rings E. Ordered integral domains F. Polynomial rings G. Finite fields

Note: Some topics (i.e. factor structures) may be treated as a separate unit rather than being done in each algebraic structure.

IX. Evaluation: Homework sets, exploratory projects, two tests and a final exam.

SAMPLE GRADING SCHEME: 10 Homework sets 100 points each 1000 2 Exams 200 points each 400 1 Exploratory project (2 for grad students) 200 points each 200/400 Final Exam 400 points for undergraduates 200 points for graduates students 200/400ˇ Total Points 2000 The exploratory project involves an investigation into an algebra problem and an essay write up of the study. It may involve using abstract algebra software such as Magma, Gap, or Maple. The graduate students have a larger percent of his/her grade based on this exploration and initiates two projects, not just one. X. Bibliography:

Bhattacharya, P.B., Jain, S. K., Nagpaul, S.R., Basic Abstract Algebra, 2nd ed., Cambridge

University Press, 1993. ˇ Birkhoff, G., and MacLane, S., A Survey of Modern Algebra, MacMillan Co., 1941. Burton, D. M., Introduction to Modern Abstract Algebra, 3rd ed., Addison-Wesley, 1988. ˇ Childs, L. N., A Concrete Introduction to Higher Algebra, Springer-Verlag, 1995.

Dubinsky, E. and Leron, U. Learning Abstract Algebra with ISETL, Springer-Verlag, 1994.ˇ Fraleigh, J. B., A First Course in Abstract Algebra, 4th ed., Addison-Wesley, 1989. Rotman, J. J., An Introduction to the Theory of Groups, 4th ed., Springer-Verlag, 1995. Stillwell, J., Elements of Algebra, Springer-Verlag, 1994.

Syllabus prepared by: Ken Smith October 13, 1995

CENTRAL MICHIGAN UNIVERSITY COLLEGE OF ARTS AND SCIENCES

COURSE SYLLABUS MTH 551 Number Systems for Elementary Mathematics Teachers 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description:

Continuation of 151. Integers, real numbers, mathematical sentences, number theory, mathematical systems. Credit will not apply toward master's degree in mathematics.

II. Prerequisites:

MTH 107 and MTH 152. III. Rationale for Course Level:

This course should be available for inservice elementary teachers as well as on-campus students.

IV. Textbooks and Other Materials to be Furnished by the Student:

Mathematical Ideas (7th Edition). Harper Collins, 1994. V. Special Requirements of the Course:

Students will need to buy at least five high density floppy disks (@ $1.00 each) and will need to bring a graphics calculator.


Lecture, cooperative learning strategies, demonstration, discussion, supplementary reading materials.

VII. Course Objectives:

To continue the development of systems of numbers which began in Mathematics 151. Emphasis is given to integers, rational numbers, and real number systems. A further objective is to relate an understanding of number systems and their properties to the teaching of elementary school mathematics. Procedures and strategies for teaching school mathematics are presented. Problems that arise in developing mathematical concepts, language and relationships are examined. Students will use algebra and other mathematical knowledge in problem solving and applications. The students will formulate and solve rich real world problems.


Unit 1 Set Theory 2 weeks Unit 2 Logic 3 weeks Unit 3 Number Theory 2 weeks Unit 4 Problem Solving 3 weeks Unit 5 Number Systems 2 weeks Unit 6 Applications/Algebra 2 weeks

IX. Evaluation:

2-3 examinations 4-5 quizzes 1-2 curriculum projects problem solving with technology, various reports on reading assignments.

Graduate students can be assigned additional challenging problems or can be required to write a short term paper. X. Bibliography:

1. Alberta Teacher's Association, Problem Solving in the Mathematics Classroom, Monograph #7, 1982.

2. Billstein, Lebeskind, Lott, A Problem Solving Approach to Mathematics for Elementary School Teachers, Benjamin Cummings, 1984.

3. Dromey, R.G., How to Solve it by Computers, Prentice Hall, 1982. 4. Heintz, Ruth E., Mathematics for Elementary Teachers, Addison-Wesley,

1980. 5. Krulik, Stephen and Rudnick, Jesse, Problem Solving, a Handbook for

Teachers, Allyn and Bacon, 1980. 6. Monograph No. 19, MCTM Problem Book, Michigan Council of Teachers

of Mathematics, 1985. 7. National Council of Teachers of Mathematics, Mathematics for the

Middle Grades 5-9 (1982 Yearbook), 1982. 8. National Council of Teachers of Mathematics, A Sourcebook of

Applications of School Mathematics, NCTM, 1980. 9. National Council of Teachers of Mathematics. Computers in Mathematics

Education (1984 Yearbook). NCTM, 1984. 10. National Council of Teachers of Mathematics. Calculators in

Mathematics Education (1992 Yearbook). NCTM, 1992. 11. National Council of Teachers of Mathematics. Guidelines for the

Preparation of Teachers of Mathematics. NCTM, 1984. 12. Sonnabend, T., Mathematics for Elementary School Teachers, Saunders

College Publishing, 1994. Syllabus prepared by Dennis St. John Name Signature October 13, 1995 Date



Probability and Statistics for MTH 554 Elementary and Middle School Teachers 3(3-0)D_ Desig. No. Title Credit/Mode I. Bulletin Description: Examines experimental probability and statistics suitable for elementary and middle school. Data gathering, organizing and presenting. Credit will not apply toward Master’s degree in mathematics. II. Prerequisites: MTH 107 and 152 III. Rationale for Course Level: Course is taken by elementary education majors and minors and by some graduate students (teachers certifying to teach mathematics or working on Masters degrees in education. IV. Textbooks and Other Materials to be Furnished by the Student: Granadeesikan, Landwehr, et al., Quantitative Literacy Series, Dale Seymour Publications, 1986; and Huff, How to Lie with Statistics, Norton, 1993. V. Special Requirements of the Course: None. VI. General Methodology Used in Conducting the Course: Small group activities and projects, with some lecture and large group discussion. VII. Course Objectives:

(1) To understand the role of statistics in our lives and how data analysis can be introduced in the elementary and middle school programs. Students will experience data gathering from surveys and experimentation.

(2) To learn some common statistical uses such as graphing and descriptive statistics

(measures of central tendency and measures of dispersion.)

(3) To learn about probability and how it can be taught to elementary and middle school

children, including the use of Monte Carlo simulation. (4) To learn to find probabilities using probability rules and using Pascval’s triangle. (5) To compare experimental and theoretical probabilities.

VIII. Course Outline: A. Introduction to Probability and Statistics.

1. Role in our lives. 2. Population vs. sample. 3. Random samples. 4. Experimental and simple theoretical probability 5. Odds. 6. Counting rules. 7. Sample spaces and events (3 weeks)

B. Data Gathering and Data Organization.

1. Bar graphs. 2. Pictographs. 3. Circle graphs. 4. Stem and leaf plots. 5. Descriptive statistics (mean, median, mode, range, IQR, standard deviation). 6. Box and whisker plots 7. Correlation and scatter plots (5 weeks)

C. Compound Probability

1. Using Pascal’s triangle. 2. Using probability rules. (2 1/2 weeks)

D. Monte Carlo Simulation (2 1/2 weeks) E. Applications of Probability & Statistics

1. Use of Punnett Squares in genetics 2. Introduction to the normal distribution (2 weeks)

IX. Evaluation: Two exams plus a final exam. Quizzes, written and oral projects.

Graduate students can be assigned additional challenging problems or can be required to write a short term paper.

X. Bibliography:

1. Curriculum and Evaluation Standards for School Mathematics, NCTM, 1989.

2. Hirsch, Activities for Implementing Curricular Themes from the Agenda for Action,

NCTM, 1986.

3. Shulte and Smart, Teaching Statistics and Probability, 1981, NCTM Yearbook, NCTM, 1981.

4. Sovchik, Teaching Mathematics to Children, 2nd ed., Harper Collins, 1996.

5. Zawojewski, Curriculum and Evaluation Standards for School Mathematics, Agenda

Series Grades 5-8, Dealing with Data and Chance, NCTM, 1991.

Syllabus prepared by: Martha Frank____________________________ Name _____________________________________ Signature December 1, 1995_______________________ Date


COURSE SYLLABUS MTH 556 Microcomputers for Elementary Mathematics Teachers 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description:

Develops the use of microcomputers in elementary education with particular emphasis on mathematical applications. Computer literacy and BASIC Programming are included.

II. Prerequisites:

107 and 251 or equivalent. III. Rationale for Course Level:

This course should be available for inservice elementary teachers as well as on-campus students.

IV. Textbooks and Other Materials to be Furnished by the Student:

ClarisWorks for Macintosh, by Fritz J. Erickson, McGraw Hill, 1994. True BASIC, Student Edition. True BASIC Inc., 1993.

V. Special Requirements of the Course:

Students will need to buy at least five high density floppy disks (@ $1.00 each) and will need to bring a graphics calculator.


Formal lecture combined with "hands-on" approach to learning about microcomputers and graphing calculators. Students will have to write programs, use software packages and create instructional materials. Cooperative learning strategies, demonstration, discussion, supplementary reading materials will also be used.

VII. Course Objectives:

The course is designed to have students investigate many of the possible uses for the computer and graphics calculator. Students will learn how these tools can be used to enhance instruction, solve problems, and create new knowledge. Students will become knowledgeable about computer literacy, computer and calculator programming, and specialized software applications for the elementary mathematics classroom. Students will, throughout the course, have opportunities to develop and explain programs and strategies for problem solving, collect, analyze, interpret, and present data,


Unit 1 Computer Literacy How a micro-computer system functions (2 weeks) Computer terms and vocabulary Hard/software demonstrations Auxiliary equipment Functions, selection and care of computers

Unit 2 Programming Micro Computers and Graphics Calculators

Introduction to BASIC (1 week) Introduction to Graphics Calculator programming (1 week) Beginning programming (2 weeks) Advanced programming (2 weeks)

Unit 3 Applications of Micro-Computers in Elementary Education

Demonstrations of word processors, mail processors, (2weeks) data bases, spreadsheets, and the internet Graphics and sound (1 week)

Unit 4 Micro-Computers and Graphics Calculator Curriculum Issues and Uses as a

Teaching Tool Problem solving in mathematics (2 weeks) Using micro-computers for problem solving (1 week) Exploring mathematical tools (Cabri, Sketchpad) (1 week)

IX. Evaluation:

2-3 examinations 2-4 written programs 1-2 curriculum projects problem solving with technology, various reports on reading assignments.

Graduate students can be assigned additional challenging problems or can be required to write a short term paper.

X. Bibliography:

1. Alberta Teacher's Association, Problem Solving in the Mathematics Classroom, Monograph #7, 1982.

2. Bent, R.J. an G.C. Setlanes, BASIC - An Introduction to Computer

Programming with the Apple, Brooks/Cole, 1983. 3. Coburn, Kelman, Roberts, Snyder, Watt and Weiner, Practical Guide to

Computers in Education, Addison Wesley, 1982. 4. Culp, George and Herbert Nickles, An Apple for the Teacher,

Brooks/Cole, 1983. 5. Department of Education, Microcomputers in Education - Uses for the

80's, Edited by N.R. Watson, Tepe, Arizona, 1982. 6. Dromey, R.G., How to Solve it by Computers, Prentice Hall, 1982. 7. Harper, D.O. and J.H. Stewart, Run: Computer Education, Brooks/Cole,

1983.

8. Jonassen, David H., Instructional Designs for Microcomputer Courseware. Lawrence Erlbaum Associates, 1988.

9. Jones, Richard M., Introduction to Computer Applications Using BASIC,

Allyn and Bacon, 1981. 10. Krulik, S. Rudnick, J.A., Problem Solving, A Handbook for Teachers,

Allyn and Bacon, Boston, 1980. 11. Mandell, Steven L., Introduction to BASIC Programming, West, 1982. 12. Michigan Council of Teachers of Mathematics. Computers in the

Mathematics Classroom, Monograph #17, 1982. 13. Moulton, Peter, Foundations of Programming through BASIC, John

Wesley & Sons, 1979. 14. National Council of Teachers of Mathematics. Computers in Mathematics

Education (1984 Yearbook). NCTM, 1984. 15. National Council of Teachers of Mathematics. Calculators in

Mathematics Education (1992 Yearbook). NCTM, 1992. 16. Posamentier, A.S., S.E. Moresh and G.H. Elgarten, Using Computers in

Mathematics, Addison-Wesley, 1983. Syllabus prepared by Dennis St. John Name Signature October 13, 1995 Date

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Course Syllabus Form: MTH 566 Course Designator & Number Mathematics Arts and Sciences Department School MTH 566 Microcomputers for Secondary Mathematics 3 Designator Number Title Credit Cross Reference Prerequisites: MTH 223 or equivalent Title Abbreviation: M I C R O S E C M T H T C H R S (Title abbreviation restricted to twenty (20) characters and spaces or less.) X Course number has been cleared with the Registrar's Office. State rationale for course level: Technology has significantly changed the way mathematics is taught and learned in secondary mathematics classrooms. This course helps secondary Mathematics Education majors and minors understand and effectively use microcomputers and graphing calculators that are appropriate for the secondary mathematics classroom. The course is also appropriate for MAT degree students who want to keep abreast of the technological changes occurring in the secondary schools. Bulletin description: (25 words or less) This course examines the use of microcomputers with appropriate software and graphing calculators to teach and learn mathematics in the secondary classroom. Textbooks and other required material to be furnished by the student: One textbook in applications of computers in secondary mathematics education One textbook in applications of graphics calculators in secondary mathematics education An appropriate graphics calculator Special requirements of the course (field trips, special fees, etc.): Students will use microcomputer laboratories on campus. General methodology used in teaching the course: The lecture/discussion class format, combined with hands-on computer learning and cooperative group work, will be used throughout. Students will solve mathematical problems using technology, prepare instructional material, review and report on current literature, write programs, and learn to use a variety of instructional and teacher centered software. Course outline: Please attach a detailed outline of the course, including its objectives, and a bibliography. If the course is divided into clearly defined topics or units, indicate the approximate number of weeks devoted to each. Evaluation: How is the student's work evaluated and how frequently? During the semester, students will have 1 -3 examinations (40-60%), 2 - 8 written assignments (25-50%), 1-2 curriculum projects (20-40%), and 2-6 journal reports (10-30%).

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Syllabus prepared by Charles Vonder Embse Date September 15, 1995

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Course Goals

For the purposes of the following descriptions and objectives, the term "microcomputer" includes all types of personal computer systems and graphics calculators.

1. To become familiar with the operation of appropriate software packages and the classroom use of these packages for teaching and learning mathematics at the secondary level.

2. To learn how to use microcomputer technology to explore, investigate, and solve problem, including problems situations that cross other disciplines than mathematics, such as science, social science, and business.

3. To learn how to use the microcomputer to be a more productive teachers through functions such as record keeping, lesson preparation, effective communications with students, colleagues, administration, and parents, and world-wide communications.

4. To prepare lessons that utilize microcomputer technology to teach mathematical concepts, investigate and solve problems, explore new patterns and relationships, model mathematical processes and realistic problems, and analyze data from real-world problem setting.

5. To prepare prospective teachers who can communicate in oral and written from about and with microcomputers and who can create a learning environment in the secondary classroom in which students with diverse learning styles can use microcomputer to prepare and communicate important mathematical ideas.

6. To learn to use the microcomputer as a tool to promote mathematical thinking, reasoning, and communications through the in-depth study of mathematical concepts and processes.

Course Outline

I. Personal Productivity Tools for Teachers 2 weeks A. word processors and mathematics text tools B. drawing programs C. grade keeping programs D. spreadsheets E. link programs connecting computers and calculators

II. Interactive Geometry Software-Operation and Classroom Use 2 weeks A. operation of Cabri Geometry II and/or Geometer's Sketchpad type programs B. classroom issues involving discovery learning using interactive geometry tools C. problem solving using interactive geometry software-geometry and algebra D. interactive geometry software as a personal productivity tool for teachers E. communicating mathematical ideas through interactive geometry software F. investigation and exploration techniques for extending problem situations

III. Mathematical Problem Solving using Microcomputers 3 weeks A. graphical solution techniques for equations and inequalities B. numerical solution techniques for equations and inequalities C. solving problems using table building functions and spreadsheets D. solving problems using student-written computer/graphics calculator programs E. using problem solving teaching methods in the mathematics classroom

IV. Statistics, Data Analysis, and Modeling 2 weeks A. descriptive statistics using computers and graphics calculators

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B. analyzing real-world data from many disciplines with computers and graphics calculators C. modeling using regression analysis/lines of best fit (theory and practice) D. using models to explain, predict, and forecast E. teaching mathematical concepts using data analysis techniques

V. Probability Simulations 2 weeks A. random number generators on a microcomputer/operations and classroom use B. modeling probability problems with a micocomputer C. conducting probability experiments D. comparing theoretical and experimental results of probability situations E. classroom issues related to probability simulations

VI. Mathematical Application Programs-Operation and Classroom Use 2 week A. computer algebra systems B. spreadsheets C. matrix manipulation systems D. 3-D graphing systems E. parametric, polar, and sequence graphing systems

VII. Mathematical Connections with Other Disciplines 2 weeks A. science connections through real-time data collection systems B. gathering and analyzing social science data C. gathering and analyzing business data

VIII. Literature Review 1 week A. search the current literature for relevant publications on the classroom use of computer and graphing calculator technology B. communicate information about the current literature in both oral and written format

IX. Curriculum Projects 2 weeks A. create curriculum materials that utilize computers and graphing calculators through individual and group assignments B. present curriculum projects in both oral and written format C. critique curriculum material presented by peers

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Bibliography Assessment Standards for School Mathematics (1995). Reston, VA: National Council of Teachers of

Mathematics. Brueningsen, C., W. Bower, L. Antinone, and E. Brueningsen (1995). Real-World Math with the CBL

System. Dallas, TX: Texas Instruments, Inc. Burrill, G. and P. Hopfensperger (1993). Exploring Statistics with the TI-81. Reading, MA: Addison-

Wesley Publishing Co. Burrill, G., J. Burrill, P. Coffield, G. Davis, J. de Lange, D. Resnick, M. Siegel (1992). Data Analysis

and Statistics Across the Curriculum. Reston, VA: National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (1989). Reston, VA: National Council

of Teachers of Mathematics. Demana, F., B. Waits, C. Vonder Embse, and G. Foley (1992). Graphing Calculator and Computer

Graphing Laboratory Manual, Second Edition. Reading, MA: Addison-Wesley Publishing Co. Froelich, G., K. Bartkovich, P. Foerster (1991). Connecting Mathematics. Reston, VA: National

Council of Teachers of Mathematics. Hansen, V. (Editor) (1984). Computers in Mathematics Education: 1984 Yearbook. Reston, VA:

National Council of Teachers of Mathematics. Heid, M. K., J. Choate, C. Sheets, R. M. Zbiek, (1995). Algebra in a Technological World. Reston,

VA: National Council of Teachers of Mathematics. Hirsch, C. (Editor) (1992). Calculators in Mathematics Education: 1992 Yearbook. Reston, VA:

National Council of Teachers of Mathematics. House, P. (Editor) (1995). Connecting Mathematics across the Curriculum: 1995 Yearbook. Reston,

VA: National Council of Teachers of Mathematics. Merris, R. (1984). Introduction to Computer Mathematics. Rockville, MD: Computer Science Press. Professional Standards for Teaching Mathematics (1991). Reston, VA: National Council of Teachers

of Mathematics. Peitgen, H., H. Jürgens, D. Saupe (1992). Fractals for the Classroom, Part One. New York, NY:

Springer-Verlag, Inc. Rubin, C. (1994). The Macintosh Bible Guide to ClarisWorks 2.1. Berkeley, CA: Peachpit Press, Inc. Vonder Embse, C. and E. Olmstead (1992). Exploring Algebra with the TI-81. Reading, MA:

Addison-Wesley Publishing Co. Vonder Embse, C. and A. Engebretsen (1994). Explorations for the Mathematics Classroom using

Cabri Geometry II. Dallas, TX: Texas Instruments, Inc. Vonder Embse, C. and A. Engebretsen (1996). Explorations for the Mathematics Classroom using TI-

92 Geometry. Dallas, TX: Texas Instruments, Inc.

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COURSE SYLLABUS STA 382 Elementary Statistical Analysis 3(3-0) Desig. No. Title Credit/Mode I. Bulletin Description:

An introduction to statistical analysis. Topics will include descriptive statistics, probability, sampling distributions, statistical inference, and regression. Greater emphasis than STA 282 will be placed on probability theory and probability distribution. Credit may not be earned in both STA 282 and STA 382.

II. Prerequisites: MTH 130 III. Rationale for Course Level: IV. Textbooks and Other Materials to be Furnished by the Student: Larson and Marx, Statistics, Prentice Hall, 1990. V. Special Requirements of the Course: Scientific Calculator. VI. General Methodology Used in Conducting the Course: Lecture, problem solving, and discussion. VII. Course Objectives: XII. To acquaint the student with the principles and the methodology of statistical

inference. XIII. To enable the student to recognize statistical problems and the necessity of

professional consultation. XIV. To enable the student to read and understand published statistical research. XV. To interest students in stuyding further in the field of statistics. VIII. Course Outline: 1. Introduction, Descriptive Statistics, and Probability 4 weeks

12. Objectives and definitions of statistics.

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13. Measures of central tendency and graphical methods. 14. Sample of space and vents 15. Probability of an event. 16. Counting rules. 17. Probability rules 18. Bayes’ Rule.

2. Random Variables, Probability Distribution 4 weeks

j. Definitions. k. Expectation and variance l. Binomial distribution. m. Other discrete probability distributions. n. Continuous probability distributions. o. Uniform, normal distributions.

I. Estimation and Testing Hypothesis for Binomial Parameter and

Normal Probability Distribution 4 weeks 4) Null and alternative hypothesis. 5) Types of errors. 6) Power functions. 7) Steps in testing hypotheses 8) Normal approximation to binomial. 9) Distribution of sample means. 10) Sampling distributions and random samples

4. Statistical Inference, Regression, and Correlation 4 weeks

G. Point and interval estimates. H. Small sample inference – “t” distribution. I. Sample size. J. Two population inference.

16. u1 – u2 17. 2. p1 – p2

L. Linear regression model. M. Inference for regression model. N. Correlation.

IX. Evaluation: Four tests and graded homework. A test approximately every four weeks.. XII. Bibliography:

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Devore, J.L., Probability and Statistics for Engineering and the Sciences, Brooks And Cole, 3rd edition, 1991. Hogg, R.V., Ledolter, J., Applied Statistics for Engineers and Physical Scientists, MacMillan, 2nd. Edition, 1992. Larson, R.I., Marx, M.L., Statistics, Prentice Hall, 1990. Mendenhall, W., Sincich, T., Statistics for Engineering and the Sciences, 3rd. edition, 1991. Netter. J. Wassermanm. W., Whitmore, G., Applied Statistics, Allyn & Bacon, 4th Edition, 1993. Rustage, J.S., Introduction to Statistical Methods, Rowman & Allanheld, Volume 1, 1984 Snedecor, G.W., Cochran, W.G., Statistical Methods, Iowa State University Press, 7th edition, 1978. Walpole, R.E., Myers, R.H., Probability and Statistics for Engineers and Scientists, MacMillan, 4th edition, 1989.

Syllabus prepared by: Carl Lee ________________________________________________ Signature September 11, 1998 Date STA382

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