# Mathematics

## Option A

**Algebra**

- By examination with focus areas in
- Exponentiation
- Factoring
- Long division
- Fundamental Theorem of Algebra
- Summation
- Induction proofs
- Complex numbers

**Euclidean Geometry**

- By examination

**Trigonometry**

- By examination with focus areas in
- Pythagorean Theorem and its converse
- Law of Cosine
- Derivation of commonly used trigonometric values
- Derivation of commonly used identities
- Development of trigonometric functions
- Degrees vs. radians
- Periodicity

- Resources: any textbook on trigonometry, for example
*Trigonometry*by Swokowski, Prentice-Hall Publishers

**Discrete/Finite Math**

- MA 2201 Discrete Mathematics

**Introductory Calculus through Integration**

- MA 1021 Calculus I
- MA 1022 Calculus II

**History of Mathematics**

- Focus areas in
- Ancient Greece
- Deductive reasoning
- Pythagorean geometry
- Conic sections

- Fermat and FLT
- Descartes and analytic geometry
- Newton, Leibniz and the rise of Calculus Bernoullis
- Gauss
- Non Euclidean Geometry

- Ancient Greece
- Resources
*An Introduction to the History of Mathematics*by Howard Eves, Holt, Rinehart and Winston*Men of Mathematics*by E. T. Bell*Classics of Mathematics*by Ronald Calinger (ed) by Prentice Hall*Mathematical Thought from Ancient to Modern Times*by Morris Kline, Oxford Press- video:
*The Proof*Nova Videos (WGBH) *Fermat's Enigma*by Simon Singh, Doubleday- http://www-history.mcs.st-and.ac.uk.history

**Use of Technology**

- Successful completion of Maple labs in Calculus I-IV sequence
- Demonstrated competency with Geometer's Sketchpad
- Demonstrated competency with Graphing Calculators

## Option B

**Abstract Algebra**

- MA 3821 Modern

**Number Theory**

- Independent study and examination in
- Division
- Divisibility and factorization
- Fundamental Theorem of Arithmetic
- Euclid's Algorithm
- Diophantine Equations
- Integer arithmetic and algebra modulo n

- Resources
*Number Theory*by David Burton (4th edition)

**or**Math 126 Elementary Number Theory at Clark University

**Calculus through Differential Equations**

- MA 1021 Calculus I
- MA 1022 Calculus II
- MA 1023 Calculus III
- MA 1024 Calculus IV
- MA 2051 Differential Equations

**Probability and Statistics**

- MA 2611 Applied Statistics I
- MA 2612 Applied Statistics II

**Non Euclidean and Transformational Geometries**

- Independent study and examination in
- Review of Euclidean geometry
- Implications of no Parallel Postulate
- Deduction in mathematics
- Hyperbolic geometry
- Elliptic geometry
- Relation to space-time physics and general relativity

- Resources
*An Introduction to Differential Geometry*by Eisenhart, Princeton University Press*An Introduction to Non Euclidean*Geometry by Harold Wolfe, The Dryden Press, New York

- or Math 128 Modern Geometry at Clark University

**Applied Mathematics/Modeling**

- MA 3431 Mathematical Modeling with Ordinary Differential Equations