Download MASTER OF ARTS IN MATHEMATICS EDUCATION (M

Year 1
Year 2
Fall
Calculus I
Calculus II
Probability and Statistics I
Probability and Statistics II
Winter
Calculus III
Multivariable Calculus
Abstract Algebra I
Abstract Algebra II
Summer
Discrete Mathematics
Real Analysis
Geometry
History of Mathematics
The two courses offered each quarter will run will in sequence and not
simultaneously.
Course Titles and Descriptions
Math 615: Calculus for Advanced Placement Teachers - I
Linear, exponential, logarithmic, power, and trigonometric functions from
algebraic, numerical, and graphical perspectives. Limits, continuity, and the
derivative. Graphing technology will be used. Advanced placement exams
will be examined with applications to classroom teaching. Prerequisites –
approval of the M.A.M.Ed. director.
Math 616: Calculus for Advanced Placement Teachers - II
A continuation of Math 615 - applications of the derivative, the definite
integral, Riemman sums, techniques of integrations, numerical integration
using graphing calculators, and applications of the integral. Prerequisite –
Math 615.
Math 617: Calculus for Advanced Placement Teachers - III
A continuation of Math 616 - infinite series and sequences, Taylor
polynomials and Taylor series, differential equations, and slope fields.
Prerequisites – Math 616.
Math 645: Multivariable Calculus for Advanced Placement Teachers
Functions of several variables, vectors, dot products and cross products,
partial differentiation, directional derivatives, optimization, Lagrange
multipliers, multiple integrals, polar and spherical coordinates. Computers
will be used to illustrate concepts. Prerequisite – Math 617.
Math 665: Discrete Structures with a Transition to Higher Mathematics
A transition to advanced courses having a greater emphasis on proof and
abstraction. Techniques of proof, logic, sets and functions, number theory,
recursive sequences, mathematical induction, and an introduction to
combinatorics. Prerequisites – approval of the M.A.M.Ed. Director.
Math 685: Real Analysis
To better prepare teachers of A.P. Calculus, the theoretical foundations of
calculus are examined. An in depth look at fundamental results in calculus
such as the Intermediate Value Theorem, the Extreme Value Theorem, the
Mean Value Theorem, the Fundamental Theorem of Calculus, Taylor’s
Theorem, and L’Hopital’s Rule. Prerequisite – Math 617 and Math 665.
Math 655: Probability and Statistics for Advanced Placement Teachers
-I
Combinatorics, sets, probability, random variables, distribution and
density functions, standard probability laws, jointly distributed random
variables. Advanced placement exams will be examined with applications to
classroom teaching. Prerequisite – Math 665.
Math 656: Probability and Statistics for Advanced Placement Teachers
- II
A continuation of Math 656 - central limit theorem, point and interval
estimation of parameters, hypothesis testing, least squares, and regression.
Prerequisite – Math 655.
Math 675: Abstract Algebra - I
Integers, rational numbers, real numbers, complex numbers, fundamental
theorem of algebra, modular arithmetic, polynomials rings, roots of
polynomials of small degree, and values of trigonometric functions. This
course provides the theoretical foundation for many topics covered in high
school mathematics courses. Prerequisite – Math 665.
Math 676: Abstract Algebra - II
A continuation of Math 675 – topics include group theory, vector spaces,
difference functions, partial fraction decomposition, introduction to Galois
theory, geometric constructions, and the insolvability of the quintic.
Prerequisite – Math 675.
Math 625: Geometry
Axiom systems, types of reasoning used in proofs, Euclidean geometry
results with concentration on triangles and circles, introduction to nonEuclidean geometry, and introduction to geometry classroom software.
Prerequisite – Math 665.
Math 635: History of Mathematics
Classical problems from number theory, algebra, Euclidean and nonEuclidean geometry, set theory, probability, and the development of
calculus. There will be an emphasis on the historical aspects of mathematics
and the solution of concrete problems. Prerequisite – Math 665.