Mathematics

Option A

Algebra

  1. By examination with focus areas in
    1. Exponentiation
    2. Factoring
    3. Long division
    4. Fundamental Theorem of Algebra
    5. Summation
    6. Induction proofs
    7. Complex numbers

Euclidean Geometry

  1. By examination

Trigonometry

  1. By examination with focus areas in
    1. Pythagorean Theorem and its converse
    2. Law of Cosine
    3. Derivation of commonly used trigonometric values
    4. Derivation of commonly used identities
    5. Development of trigonometric functions
    6. Degrees vs. radians
    7. Periodicity
  2. Resources: any textbook on trigonometry, for example Trigonometry by Swokowski, Prentice-Hall Publishers

Discrete/Finite Math

  1. MA 2201 Discrete Mathematics

Introductory Calculus through Integration

  1. MA 1021 Calculus I
  2. MA 1022 Calculus II

History of Mathematics

  1. Focus areas in
    1. Ancient Greece
      1. Deductive reasoning
      2. Pythagorean geometry
      3. Conic sections
    2. Fermat and FLT
    3. Descartes and analytic geometry
    4. Newton, Leibniz and the rise of Calculus Bernoullis
    5. Gauss
      1. Non Euclidean Geometry
  2. Resources
    1. An Introduction to the History of Mathematics by Howard Eves, Holt, Rinehart and Winston
    2. Men of Mathematics by E. T. Bell
    3. Classics of Mathematics by Ronald Calinger (ed) by Prentice Hall
    4. Mathematical Thought from Ancient to Modern Times by Morris Kline, Oxford Press
    5. video: The Proof Nova Videos (WGBH)
    6. Fermat's Enigma by Simon Singh, Doubleday
    7. http://www-history.mcs.st-and.ac.uk.history

Use of Technology

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

Option B

Abstract Algebra

  1. MA 3821 Modern

Number Theory

  1. Independent study and examination in
    1. Division
    2. Divisibility and factorization
    3. Fundamental Theorem of Arithmetic
    4. Euclid's Algorithm
    5. Diophantine Equations
    6. Integer arithmetic and algebra modulo n
  2. Resources
    1. Number Theory by David Burton (4th edition)
  3. or Math 126 Elementary Number Theory at Clark University

Calculus through Differential Equations

  1. MA 1021 Calculus I
  2. MA 1022 Calculus II
  3. MA 1023 Calculus III
  4. MA 1024 Calculus IV
  5. MA 2051 Differential Equations

Probability and Statistics

  1. MA 2611 Applied Statistics I
  2. MA 2612 Applied Statistics II

Non Euclidean and Transformational Geometries

  1. Independent study and examination in
    1. Review of Euclidean geometry
    2. Implications of no Parallel Postulate
    3. Deduction in mathematics
    4. Hyperbolic geometry
    5. Elliptic geometry
    6. Relation to space-time physics and general relativity
  2. Resources
    1. An Introduction to Differential Geometry by Eisenhart, Princeton University Press
    2. An Introduction to Non Euclidean Geometry by Harold Wolfe, The Dryden Press, New York
  3. or Math 128 Modern Geometry at Clark University

Applied Mathematics/Modeling

  1. MA 3431 Mathematical Modeling with Ordinary Differential Equations 
 
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