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Mathematics Course Information

Mathematics Courses

100 Calculus with Algebra I 3 cr.
Initial topics of 111 with topics from algebra integrated as needed. Credit is not allowed for both 100/104, 100/111, or 100/115. Example syllabus.
104 Calculus with College Algebra and Trigonometry I 4 cr.
Initial topics of 115 with topics from algebra and trigonometry integrated as needed. Credit is not allowed for both 104/100, 104/111, or 104/115. Example syllabus.
110 Calculus with Algebra II 3 cr.
Remaining topics of 111 with topics from algebra integrated as needed. Credit is not allowed for both 110/114, 110/111, or 110/115. Prerequisite: "C" or better in 100. Example syllabus.
111 Calculus for Non-science Students 3 cr.
Limits, continuity, differentiation of algebraic, exponential and logarithmic functions. An introduction to integration. Credit is not allowed for both 111/100, 111/110, 111/104, 111/114, or 111/115.
114 Calculus with College Algebra and Trigonometry II 4 cr.
Remaining topics of 115 with topics from algebra and trigonometry integrated as needed. Credit is not allowed for both 114/110, 114/111, 114/115. Prerequisite: "C" or better in 104. Example syllabus.
115 Calculus I 4 cr.
The same topics as 111 except trigonometric functions are included. Credit is not allowed for both 115/100, 115/110, 115/104, 115/114, or 115/111. Example syllabus.
116 Calculus II 4 cr.
Applications of the definite integral, parametric equations, polar coordinates, sequences, and series. Prerequisite: "C" or better in 114 OR 115. Example syllabus.
125 Fundamentals of Statistics 3 cr.
Exploratory data analysis and statistical inference including graphical summaries of data, sampling distributions, confidence intervals, and hypothesis testing. Credit not allowed for both 125/225. Example syllabus.
135 Discrete Mathematics 3 cr.
Sets, functions, relations, partial order, methods of propositional logic, introduction to predicate logic, counting, recurrence relations, asymptotic analysis, proof, including induction, introduction to probability, graphs. Example syllabus.
215 Calculus III 4 cr.
Calculus of functions of several variables and vector valued functions. Line and surface integrals. Prerequisite: 116. Example syllabus.
220 Proof Writing Seminar 1 cr.
The purpose of this course is to introduce students to various mathematical proof techniques including conditional proofs, biconditional proofs, proofs by contradiction, induction, and double inclusion. The goal of the course is that the students become more proficient at proof-writing in order to make more seamless the transition to higher level mathematics. Prerequisite: Math 116; Co-requisite: Math 135
225 Introduction to Biostatistics 3 cr.
Descriptive statistics, sampling distributions, confidence intervals, hypothesis testing, non-parametric methods, chi-square tests, regression and correlation methods, and analysis of variance. Credit is not allowed for both 125/225. Prerequisite: Evidence of college level algebra skills. Example syllabus.
301 Introduction to Probability and Statistics I 3 cr.
Univariate and multivariate probability distributions of discrete and continuous random variables, mathematical expectation, limit theorems. Prerequisite: 116. Example syllabus.
302W Introduction to Probability and Statistics II 3 cr.
A continuation of 301 including probability and sampling distributions of random variables, confidence intervals, and hypothesis testing. Prerequisite: 301. Example syllabus.
308 Numerical Analysis 3 cr.
Linear systems, interpolation, functional approximation, numeric differentiation and integration, and solutions to non-linear equations. May be counted as either mathematics or computer science, but not both. Prerequisites: 116 and COSC 150 or 160.
310 Linear Algebra 3 cr.
Systems of linear equations, vectors and matrices, matrix operations, determinants, vector spaces and subspaces, linear transformations, and eigenvalues and eigenvectors. Prerequisite: 116
311 Number Theory 3 cr.
Divisibility, congruences, quadratic residues, Diophantine equations, and arithmetic functions. Prerequisites: 135, 215, and 220. Example syllabus.
312 Probability for Actuarial Science 2 cr.
The course will provide an extensive discussion of topics in probability for students interested in careers in actuarial science. Particular emphasis will be given to problem solving in preparation for the first actuarial exam (Exam P/1). The topics include basic probability, Bayes' Theorem, random variables, discrete and continuous probability distributions, moment generating functions, multivariate distributions and the central limit theorem. Prerequisites: 301, 302W
314 Differential Equations 3 cr.
First-order ordinary differential equations, theory and solutions of higher order linear ordinary differential equations, the Laplace transform, numerical solutions of differential equations, applications to physical sciences and engineering. Prerequisite: 116.
320 Topics in Mathematics 3 cr.
Elementary mathematics applied to models in the natural or environmental sciences. Cannot be counted toward a major in mathematics. Prerequisite: 115. Example course syllabus, example component syllabus.
325W Applied Statistics with Regression 3 cr.
One-way, two-way analysis of variance, Latin squares, methods of multiple comparisons, analysis of covariance, balanced and unbalanced designs, linear and multiple regression. Prerequisite: 225, or 301, or permission of instructor.
330W Fundamentals of Geometry 3 cr.
Euclidean and non-Euclidean geometry from both the synthetic and metric axiomatic approach. Prerequisites: 135, 215, and 220.
335 Biostatistics II 3 cr.
This course is a continuation of Math 225 (Introduction to Biostatistics). Topics include statistical issues in diagnostic tests, contingency table analyses, multiple two-by-two table analyses, linear and multiple regression, logistic regression, survival analysis, and nonparametric statistical procedures. Example syllabus.
340 Problem Solving Seminar 1 cr.
Solution and discussion of problems from the Putnam Examination and other sources. Prerequisite: Completion of or concurrent enrollment in 215 or permission of the instructor.
345 Survival Analysis 3 cr.
Descriptive methods for survival data, survival and hazard functions, proportional and additive hazards models, parameter inference and regression diagnostics, multivariate analysis. Prerequisite: (225,335) or (301, 302W)
350W History of Mathematics 3 cr.
Multicultural survey of the history of mathematics from the development of number systems to the development of calculus. Contributions of ancient Greek and western mathematics are emphasized, but those of the Egyptian, Babylonian, Islamic, Hindu, and Chinese cultures are also discussed. Prerequisites: 135, 215, and 311. Example syllabus.
366 Operations Research 3 cr.
The course will provide an introduction to the background of operations including example problems and a brief history. An extensive discussion of the theory and applications of linear programming will follow. Other topics will include nonlinear programming, continuous and discrete probability models, dynamic programming, game theory and transportation and network flow models. Prerequisite: 116.
402W Abstract Algebra I 3 cr.
An introduction to algebraic structures: rings, ideals, integral domains, fields, and groups, as well as homomorphisms and isomorphisms. Prerequisites: 135, 215, 220, and 310. Example syllabus.
403W Topology 3 cr.
Topological spaces, homeomorphisms, connectedness, compactness, regular and normal spaces, metric spaces, convergence, and separation axioms. Prerequisites: 402W or 415W.
405 Fundamentals of Actuarial Mathematics 3 cr.
Deterministic and stochastic modeling approaches to annuities and insurance, fractional durations, continuous payments, expenses, survival distributions, constant benefit contracts, minimum failure time, risk theory for insurance contract portfolios. Prerequisites: 301, 302W or 312.
412W Abstract Algebra II 3 cr.
A deeper examination of the algebraic structures studied in 402W including quotient groups and rings, extension fields, and other selected topics. Prerequisite: 402W.
415W Introduction to Real Analysis I 3 cr.
Functions, sequences and series, limits, continuity and uniform continuity, derivatives. Prerequisites: 135, 215, 310, and 220.
416W Introduction to Real Analysis II 3 cr.
A continuation of 415W including integration theory and advanced topics in analysis. Prerequisite: 415W.
420 Introduction to Complex Variables 3 cr.
The complex number plane, analytic functions, integration of complex functions, sequences and series, and conformal mappings. Prerequisite: 415W.
425W Experimental Design 3 cr.
Factorial designs, fixed and random effects models, nested and nested-factorial designs, split-plot designs, response surface designs. Prerequisite: 325W or permission of instructor.
491-99 Selected Topics in Mathematics 1-3 cr.

Statistics Courses

 

125 Fundamentals of Statistics 3 cr.
Exploratory data analysis and statistical inference including graphical summaries of data, sampling distributions, confidence intervals, and hypothesis testing. Credit not allowed for both 125/225. Example syllabus.
225 Introduction to Biostatistics 3 cr.
Descriptive statistics, sampling distributions, confidence intervals, hypothesis testing, non-parametric methods, chi-square tests, regression and correlation methods, and analysis of variance. Credit is not allowed for both 125/225. Prerequisite: Evidence of college level algebra skills. Example syllabus.
301 Introduction to Probability and Statistics I 3 cr.
Univariate and multivariate probability distributions of discrete and continuous random variables, mathematical expectation, limit theorems. Prerequisite: 116. Example syllabus.
302W Introduction to Probability and Statistics II 3 cr.
A continuation of 301 including probability and sampling distributions of random variables, confidence intervals, and hypothesis testing. Prerequisite: 301.
325W Applied Statistics with Regression 3 cr.
One-way, two-way analysis of variance, Latin squares, methods of multiple comparisons, analysis of covariance, balanced and unbalanced designs, linear and multiple regression. Prerequisite: 225, or 301, or permission of instructor.
335 Biostatistics II 3 cr.
This course is a continuation of Math 225 (Introduction to Biostatistics). Topics include statistical issues in diagnostic tests, contingency table analyses, multiple two-by-two table analyses, linear and multiple regression, logistic regression, survival analysis, and nonparametric statistical procedures. Example syllabus.
425W Experimental Design 3 cr.
Factorial designs, fixed and random effects models, nested and nested-factorial designs, split-plot designs, response surface designs. Prerequisite: 325W or permission of instructor.

Core Courses

 

UCOR 111 Problem Solving with Creative Math 3 cr.
Learn the skills of creative problem solving strategies, logical reasoning, communication and writing focused on group interaction with a supportive environment. Explore topics in areas such as probability, statistics, graph theory, mathematics in the arts, and topics relevant to everyday life.