BA in Natural Science and Mathematics, Concentration in Mathematics, September 2011

Learning Outcomes: BA Mathematics

1:

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athe

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5: A

pply

Mat

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cept

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easo

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(In

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)

Required: M215 Calculus I, One Variable (LO 2) Calculate & Interpret Finite & Infinite Limits, Derivatives, Integrals Apply concepts of Derivatives and Integrals to Solve Applications Analyze physical phenomenon using derivatives and integrals M216 Calculus II, Sequences (LO 2) Calculate & Interpret Derivatives and Integrals including Improper Integrals of Functions

Determine the Convergence of Sequences and Series Illustrate a given Function as Expansion of an Infinite Series Math-M311 Calculus III, Several Variables (LO 2) Demonstrate an understanding of Vector Calculus Apply Partial Derivatives to Optimization Understand Multivariant Integration & its Applications

Math-M380 History of Math (LO 4) Understand the development of mathematics in various cultures Understand the history of various fields in mathematics Understand the Historical Effects of mathematics in other areas of science Understand the Historical Effects of mathematics in Liberal Arts Math-M393 Bridge to Abstract Mathematics LO 1 and LO 3 Demonstrate Basic Mathematical Logic: Propositions, Connectives, Quantifiers, Proof Techniques

Demonstrate Appropriate Use of Sets/Set Notation Define/Identify Relations: Cartesian Products, Equivalence Relations, Ordering Relations

Define/Identify Functions (Properties) Demonstrate Use of Cardinality with Respect to Sets Capstone (LO 1,2,3) Demonstrate an understanding of basic proof methods (e.g. induction, conditionals)

Demonstrate an understanding of properties of continuous functions (e.g. Extreme Value Theorem)

Demonstrate the ability to converse about the basic ideas in one advanced field of mathematics (e.g. discuss the definition of closure in the context of point set Topology)

Must Take 6 credit hours in Following 3 Courses: Math-M303 Linear Algebra LO 5 (in Future) Demonstrate understanding of Real and Complex Vector Spaces and Linear Transformations

Perform Operations on Matrices Solve System of Equations using Matrix Algebra

Math-M313 Differential Equations Demonstrate ability to use basic techniques to solve differential equations, analytically and numerically

Demonstrate ability to apply differential equations to problems involving models from biological and physical sciences

Math-M371 Numerical Methods Calculate & Interpret Roots, Derivatives, Integrals of function using Numerical Methods

Compare & Contrast Convergence Rates of Numerical Methods Determine Function that Fits a given set of Data points 30 Credit Hours from Following Courses: Math-M295 Readings/Research Variable Based Upon Topic Math-M312 Calculus IV Demonstrate understanding of Green’s Theorem & its Applications Demonstrate understanding of Stoke’s Theorem & its Applications Demonstrate understanding of Divergence Theorem & its Applications Math-M366 Statistical Inference Demonstrate understanding of basic Descriptive Statistics Demonstrate how to Construct Confidence Intervals Demonstrate how to Perform various Tests of Hypothesis Demonstrate understanding of Non-Parametric Statistics Demonstrate understanding of Analysis of Variance Apply Software Programs such as Stat Crunch in Analyzing Data M403 Modern Algebra I Demonstrate knowledge of Definitions of basic Algebraic Structures (Group, Ring, Integral Domain, Field)

Demonstrate ability to Prove basic Theorems in Abstract Algebra (e.g. prove: If H≤G is a normal subgroup, then G/H is a group)

Apply basic Principles of Ring Theory to prove Fermat’s Little Theorem and Euler’s Theorem

M405 Number Theory Demonstrate ability to apply Number Theory to Cryptography Demonstrate ability to apply theorems of Number Theory to questions of Divisibility and remainders

Demonstrate ability to Solve Diophantine Equations Demonstrate knowledge of History of Number Theory M406 Topics Variable Based upon Topic M413 Introduction to Analysis I Demonstrate Use of Induction as is Relates to Natural numbers Demonstrate Appropriate Use of Axioms of Real Numbers Define and Use Compactness, Completeness, Infimum, Supremum with Sets of Real Numbers

Demonstrate Knowledge of Sequences, Limits, Bolzano-Weierstrass Theorem, Subsequences

Apply Properties of Continuous and Uniformly Continuous Functions Math-M415 Elementary Complex Variables Demonstrate understanding of Representation of (sets of ) Complex Numbers in the Amagard Plane

Demonstrate the use of Differentiability Criteria to determine whether a function is Holomorphic (analytic)

Apply the Residue Theorem to evaluate Indefinite Integrals on the Real Line Apply Liouville’s Theorem to entire functions M421 Introduction to Topology

Define/Identify Basic Concepts of Topology Demonstrate Use of Subspaces and Continuity Homeomorphisms and Standard Topology of Rn Apply basic theorems about Finite Products of Topological Spaces to prove simple statements

Ability to Prove basic Consequences of Connectedness Ability to Prove basic Consequences of Compactness Ability to Prove basic Consequences of Separation Axioms Math-M447 Mathematical Models I Demonstrate ability to solve Linear and Non-Linear Programming Problems Demonstrate understanding of Principles of Operations Research Demonstrate ability to Solve Problems in Game Theory Demonstrate ability to Solve Distribution and Transportation Problems