1. Algebra
by examination
focus areas:
exponentiation
factoring
long division
the Fundamental Theorem of Algebra
summation
induction proofs
complex numbers
2. Euclidean Geometry
by examination
focus areas:
resources:
3. Trigonometry
by examination
focus areas:
the Pythagorean Theorem and its Converse
the 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; Trigonometry by Swokowski - Prentice- Hall Publishers
4. Discrete/Finite Math
MA 2201 Discrete Mathematics
5. Introductory Calculus Though Integration
MA 1021 and 1022 (Calculus I and II)
6. History of Mathematics
Focus Areas:
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
Resources:
An Introduction to the History of
Mathematics
Howard Eves, Holt, Rinehart and Winston
Men of Mathematics E.T.Bell
Classics of Mathematics Ronald Calinger (ed)
Prentice Hall
Mathematical
Thought from Ancient to Modern
Times Morris Kline, Oxford Press
video: The Proof Nova Videos (WGBH)
Fermat's Enigma Simon Singh, Doubleday
http://www-history.mcs.st-and.ac.uk.history/
7. Use of Technology
sucessful completion of Maple labs in Calculus I-IV sequence
demonstrated competency with Geometer's Sketchpad
demonstrated competency with Graphing Calculators
b) 8-12 requirements
1. Abstract Algebra
MA
3821 Modern Algebra
2. Number Theory
independent study and examination in:
Focus Areas:
division, divisibility and factorization
the 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
3. Calculus Through Differential Equations
MA 1021, 1022,1023,1024 (Calculus I-IV) and MA 2051 (Differential Equations)
4. Probability and Statistics
MA 2611 and 2612, Applied Statistics I and II
5. Non Euclidean and Transformational Geometries
independent study and examination in
focus areas:
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 NonEuclidean Geometry by Harold Wolfe, The Dryden Press, New York
or Math 128 Modern Geometry at Clark University
6. Applied Mathematics/Modeling
MA 3431 Mathematical Modeling with Ordinary Differential Equations