Subject Code: MATH, STAT • Section 9.9
Undergraduate courses offered by the faculty in Mathematics and Statistics, supporting major curricula, academic minors, and the Alkimi Core.
Catalog Documentation
Courses in Mathematics and Statistics are designed around rigorous empirical, theoretical, and applied principles. Coursework builds systematically from 100-level introductory surveys through 400-level advanced capstones and research seminars.
Prerequisites must be completed with a grade of C- or higher (unless specified otherwise by the academic department). Students who have not satisfied course prerequisites may only enroll with explicit written permission of the instructor and department chair.
Catalog Citation
Official descriptions, credit distributions, and prerequisites authorized by the Faculty Senate.
Subject Summary
Complete Listings
Mathematical modeling, percentage analysis, proportional reasoning, financial mathematics (compound interest, annuities, mortgages), probability, and descriptive statistics.
Polynomial, rational, exponential, logarithmic, and trigonometric functions, analytic trigonometry, vectors, systems of equations, and polar coordinates.
Limits, derivatives, applications of differentiation, and an introduction to integration.
Techniques of integration (parts, trigonometric substitution, partial fractions), applications of definite integrals, improper integrals, parametric curves, polar coordinates, and infinite series.
Vectors in three dimensions, vector-valued functions, functions of several variables, partial derivatives, directional derivatives, multiple integrals, Green's theorem, Stokes' theorem, and divergence theorem.
Systems of linear equations, Gaussian elimination, matrix algebra, vector spaces, subspaces, linear independence, basis, dimension, linear transformations, determinants, eigenvalues, and eigenvectors.
Propositional and predicate logic, set theory, methods of proof, mathematical induction, relations, functions, combinatorics, graph theory, and Boolean algebra.
Rigorous training in mathematical proof writing, axiomatic systems, equivalence relations, cardinality, countable and uncountable sets, and foundational analysis.
First-order differential equations, linear second-order equations, Laplace transforms, power series solutions, systems of linear differential equations, and qualitative phase-plane analysis.
Rigorous algebraic theory of groups, subgroups, cyclic groups, permutation groups, cosets, Lagrange's theorem, normal subgroups, quotient groups, homomorphisms, and introduction to rings.
Rigorous theoretical treatment of the real number system, topology of metric spaces, sequences, Cauchy sequences, limits of functions, continuity, uniform continuity, differentiation, and Riemann integration.
Independent research on an advanced mathematical topic under faculty guidance, resulting in a written senior monograph and departmental presentation.
Descriptive statistics, probability distributions, normal distributions, confidence intervals, hypothesis testing, t-tests, one-way and two-way ANOVA, chi-square tests, correlation, and simple regression.
Probability spaces, random variables, joint and conditional distributions, mathematical expectation, moment generating functions, law of large numbers, central limit theorem, and maximum likelihood estimation.
