Course Descriptions - Mathematics
Mathematics (MATH)
Faculty of Arts and Science
Mathematics 0500
Polynomials and rational functions, trigonometry, exponential and logarithmic functions, inequalities, rudiments of probability and counting.
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This course may not be taken for credit by students with Mathematics 30‑1 or Pure Mathematics 30 |
This course may not be included among the mathematics courses required for Computer Science or Mathematics majors in Arts and Science.
Mathematics 1410
Linear systems. Vectors and matrices. Determinants. Orthogonality and applications. Vector geometry. Eigenvalues, eigenvectors, and applications. Complex numbers.
Mathematics 1510
Differentiation of elementary functions, the chain and product rules, extrema problems, integration. Applications from management, humanities and the social sciences.
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Mathematics 1510 may not be counted toward the requirements for a major in Mathematics and is not suitable for students requiring more than one semester of Calculus. |
Mathematics 1560
Functions. Limits. Continuity. Differentiation and integration of polynomial, rational, root, trigonometric, exponential, and logarithmic functions. Applications of derivatives, including linear approximations and Taylor polynomials. Curve sketching and optimization. Anti-derivatives. Change of variable. Definite integrals. Fundamental Theorem of Calculus.
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Mathematics 31 and a blended grade of at least 75 percent in Mathematics 30‑1 or Pure Mathematics 30 |
Mathematics 2000
Logic, proofs. Set theory. Relations and functions. Finite and countable sets. Induction. Examples of axiomatic mathematical theories.
Mathematics 2090
Principles of Logic. Number Systems and Bases. Sets of real numbers: Integers, Rationals, Irrationals. Modular Arithmetic and applications. Divisibility, primes and elementary number theory.
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Students should not take Mathematics 2090 if they have received credit for Mathematics 2000 prior to enrolling in Mathematics 2090. |
Mathematics 2090 may not be counted toward the requirements for a major in Mathematics or Computer Science.
Mathematics 2090 is primarily intended for prospective elementary school teachers who would not ordinarily take university mathematics courses.
Mathematics 2560
Applications of integration; logarithmic, exponential, and hyperbolic functions; inverse functions; inverse trigonometric and hyperbolic functions; indeterminate forms; improper integrals; techniques of integration; polar coordinates; introduction to differential equations.
Mathematics 2570
Sequences and series, convergence tests, Taylor's series, vector-valued functions of a real variable, applications to analytic geometry, partial derivatives.
Mathematics 2580
Calculus of functions of several variables: partial differentiation, chain rule, applications, multiple integration, change of variables, theorems from vector analysis, including Stokes’ Theorem.
Mathematics 3100
First Order Logic. Validity, provability, completeness, consistency, independence, categoricity, decidability, Gödel’s Theorem.
Mathematics 3200
Introduction to classical geometry from the axiomatic point of view. Lines and affine planes. Separation, order, similarity, congruence. Isometries and their classification. Groups of symmetries. Projective, hyperbolic and inversive geometries.
Mathematics 3400
Groups, abelian groups, subgroups, quotient groups. Homomorphism. Isomorphism theorems. Lagrange’s theorem. Permutation groups. Sylow theorems. Commutative rings, subrings, ideals. Quotient rings and ideals. Polynomial rings.
Mathematics 3410
Vector spaces over the real and complex numbers. Basis and dimension. Linear transformations. Change of basis. Gram-Schmidt orthogonalization. Eigenvectors and diagonalization. Canonical forms. Cayley-Hamilton Theorem.
Mathematics 3461
Division algorithm. Fundamental Theorem of Arithmetic. Euclidean Algorithm. Linear Diophantine equations. Congruences. Chinese Remainder Theorem. Quadratic reciprocity. Additional topics such as Pythagorean triples, Gaussian integers, sums of squares, continued fractions, arithmetic functions, or cryptography.
Mathematics 3500
Rigorous treatment of the notions of calculus of a single variable, emphasizing epsilon-delta proofs. Completeness of the real numbers. Upper and lower limits. Continuity. Differentiability. Riemann integrability.
Mathematics 3560
Complex number system and complex plane. Analytic functions. Complex integration. Power series. Calculus of residues.
Mathematics 3600
First order ordinary differential equations. Second and higher order ordinary differential equations. Linear systems of ordinary differential equations. Qualitative theory of ordinary differential equations. Applications. Series solutions. Singular point expansions. Elementary linear difference equations.
Mathematics 3650
Adjoints. Oscillation theory. Matrix methods. Matrix exponential functions. Sturm-Liouville theory. Orthonormal systems and Fourier series. Eigenfunction expansions. Laplace, Fourier and Mellin transforms. Convolutions. Convergence theory. Plancherel and Parseval formulae. Distributions. Solving PDEs using integral transforms. Fundamental solutions. Separation of variables. Heat, wave and Poisson equations. Harmonic functions.
Mathematics 3850
Mathematics 3860
Mathematics 4310
Topological spaces. Topology of metric spaces. Continuity. Open covers and compactness. Separation. Connectedness.
Mathematics 4400
Polynomial rings. Fields and field extensions, construction problems. Finite fields. Galois Theory. Fundamental Theorem of Algebra.
Mathematics 4461
Mathematics 4500
Sequences and series of functions. Uniform continuity. Uniform convergence. The Stone-Weierstrass Theorem. The Lebesgue (or Riemann-Stieltjes) integral. Fourier series. Other topics.