Limits and continuity; differential calculus of functions of a single variable; the Mean Value Theorem, and determination of extrema; applications including numerical approximation methods; antidifferentiation.

Integral calculus of functions of a single variable including the Fundamental Theorem of Calculus and techniques and applications of integration; introduction to partial derivatives.

Differential calculus of the algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions of a single variable; introduction to integral calculus; techniques of integration including integration by parts; introduction to partial derivatives. Applications to problems in science are emphasized.

Numerical and graphical methods of descriptive statistics; basic probability; introduction to discrete and continuous random variables; sampling distributions, estimation and hypothesis testing; simple linear regression. Applications to problems in science are emphasized.

Differential calculus of the algebraic, exponential, and logarithmic functions of a single variable; introduction to integral calculus; introduction to the differential calculus of functions of several variables. Applications to problems in business and economics are emphasized.

Hyperbolic functions; polar coordinates and parametric equations; improper integrals; infinite sequences and series; Taylor series.

Lines, planes, surfaces and vectors in space; differential and integral calculus of functions of several variables; line and surface integrals including Green's Theorem, Stokes' Theorem and the Divergence Theorem.

First order differential equations; linear differential equations; methods of undetermined coefficients and variation of parameters; inverse differential operators; power series solutions; special differential equations such as Bessel's and Legendre's; introduction to Laplace Transforms.

Vector spaces; linear transformations and their representation by matrices; change of basis formula.

Basic counting principles; permutations and combinations, with applications; Multinominal Theorem; combinatorial identities and combinatorial arguments; recurrence relations; principle of inclusion and exclusion; pigeonhole principle.†

An introduction to game-theoretic methods and their applications. Mathematical game models are used to study problems such as the free-rider problem of economics and political science, and the choices of firms in oligopolistic markets.

Data collection and description including univariate and bivariate frequency tables, histograms, and summary statistics; elementary probability theory; random variables and expectations; sampling theory and the Central Limit Theorem; estimation and hypothesis testing for data from one and two normal populations.

Randomization and replication; completely randomized and randomized complete block designs, including analysis of variance (ANOVA) for fixed, random, and mixed effects models; efficiency of designs; multiple comparison procedures; simple linear regression model and analysis; introduction to model diagnostics.

A rigorous development of calculus. Topics include sequences, convergence, limits, continuity, differentiability and the Riemann integral.

Examples of metric spaces; basic properties of open and closed sets; convergent sequences and continuous and uniformly continuous functions; connected sets; compactness, sequential compactness and the Bolzano-Weierstrass property; completion of a metric space.††

Eigenvalues and eigenvectors; diagonalization; Cayley-Hamilton Theorem; inner product spaces.

Introduction to the construction and analysis of algorithms; describing algorithms in pseudocode; recursive procedures; complexity of functions and algorithms; study of several specific non-numerical and numerical algorithms.††

Linear programming; Simplex algorithm and applications; special linear programming problems including transportation, transshipment, optimal assignment, network flow, minimal spanning tree, shortest path, PERT, and travelling salesman; dynamic programming; introduction to integer programming and non-linear programming. Projects involving practical use of Operations Research techniques will constitute part of the course requirements.††

Discrete and continuous probability models; random variables; univariate and multivariate distributions; conditional distributions; expectation operator, moments, and moment generating functions; functions of random variables; limit theorems.†

Review of problems and objectives of parametric statistics; likelihood function; methods of finding estimators; properties of estimators; interval estimation; hypothesis testing procedures; Neyman-Pearson Lemma and likelihood ratio testing.†

Multivariate normal and Wishart distributions; estimation and hypothesis testing for data from one and two independent normal populations; classification procedures including discriminant and cluster analyses; principal component and factor analyses. Data may be processed using available statistical software packages.†

Binomial, multinominal and hypergeometric distributions; contingency tables; Wilcoxon and other non-parametric tests; simple random sampling; survey design; stratified sampling; proportional allocation; ratio estimators; cluster sampling; determination of sample size.††

Sigma-algebras of sets; set functions; outer measures, measurable sets and Lebesgue measure; Riemann and Lebesgue integrals; convergence in measure.†