Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment.

This course uses a Case-Study approach to teach statistical techniques with R: confidence intervals, hypotheses tests, regression, and anova. Also, it covers major statistical learning techniques for both supervised and unsupervised learning. Supervised learning topics cover regression and classification, and unsupervised learning topics cover clustering & principal component analysis. Prior basic statistic skills are needed.

Introduces techniques used in obtaining numerical solutions, emphasizing error estimation. Includes approximation and integration of functions, and solution of algebraic and differential equations. Prerequisite: Two years of college mathematics, including some linear algebra and differential equations, and the ability to write computer programs in any language.

Includes point estimation methods, confidence intervals, hypothesis testing for one population and two populations, categorical data tests, single and multi-factor analysis of variance (ANOVA) techniques, linear and non-linear regression and correlation analysis, and non-parametric tests. Students cannot receive credit for both this course and APMA 3110. Prerequisite: APMA 3100 or MATH 3100.

Introduces basic concepts of probability such as random variables, single and joint probability distributions, and the central limit theorem. The course then emphasizes applied statistics, including descriptive statistics, statistical inference, confidence intervals, hypothesis testing, correlation, linear regression, and ANOVA. Students cannot receive credit for both this course and APMA 3120. Prerequisite: APMA 2120 or equivalent.

Advanced Special topics in Applied Mathematics

Topics include analytic functions, Cauchy Theorems and formulas, power series, Taylor and Laurent series, complex integration, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: APMA 2120 or MATH 2310 or APMA 2512 - Honors Engineering Mathematics II.

Analyzes the role of statistics in science; hypothesis tests of significance; confidence intervals; design of experiments; regression; correlation analysis; analysis of variance; and introduction to statistical computing with statistical software libraries. Prerequisite: Admission to graduate studies.

Analyze and apply systems of linear equations; vector spaces; linear transformations; matrices; determinants; eigenvalues; eigenvectors; coordinates; diagonalization; orthogonality; projections; inner product spaces; quadratic forms; The course is both computational and applicable. MATLAB is frequently used and prior experience in MATLAB (loops, functions, arrays, conditional statements) is helpful. Prerequisite: APMA 2120 or equivalent.

The concepts of differential and integral calculus are developed and applied to the elementary functions of a single variable. Limits, rates of change, derivatives, and integrals. Applications are made to problems in analytic geometry and elementary physics.