1011Q. Introductory College Algebra and Mathematical Modeling

Emphasizes two components necessary for success in 1000-level courses which employ mathematics. The first component consists of basic algebraic notions and their manipulations. The second component consists of the practice of solving multi-step problems from other disciplines, called mathematical modeling. The topics include: lines, systems of equations, polynomials, rational expressions, exponential and logarithmic functions. Students will engage in group projects in mathematical modeling. Strongly recommended as preparation for Q courses for students whose high school algebra needs reinforcement.

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1020Q. Problem Solving

An introduction to the techniques used by mathematicians to solve problems. Skills such as Externalization (pictures and charts), Visualization (associated mental images), Simplification, Trial and Error, and Lateral Thinking learned through the study of mathematical problems. Problems drawn from combinatorics, probability, optimization, cryptology, graph theory, and fractals. Students will be encouraged to work cooperatively and to think independently. Not eligible for course credit by examination.

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1030Q. Elementary Discrete Mathematics

Topics chosen from discrete mathematics. May include counting and probability, sequences, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems, voting methods, apportionment methods, mathematics of finance, number theory.

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1060Q. Precalculus

Preparation for calculus. Review of algebra. Functions and their applications; in particular, polynomials, rational functions, exponentials, logarithms and trigonometric functions.

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1070Q. Mathematics for Business and Economics

Linear equations and inequalities, matrices, systems of linear equations, and linear programming; sets, counting, probability and statistics; mathematics of finance; applications to business and economics.

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1071Q. Calculus for Business and Economics

Derivatives and integrals of algebraic, exponential and logarithmic functions. Applications to business and economics.

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1131Q. Calculus I

Limits, continuity, differentiation, antidifferentiation, definite integral, with applications to the physical sciences and engineering sciences. Suitable for students with some prior calculus experience. Substitutes for MATH 1120Q, 1126Q, or 1151Q as a requirement. Two credits for students who have passed MATH 1125Q.

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1132Q. Calculus II

Transcendental functions, formal integration, polar coordinates, infinite sequences and series, vector algebra and geometry, with applications to the physical sciences and engineering. Substitutes for MATH 1122Q as a requirement.

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1793. Foreign Study

Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure. May count toward the major with consent of the advisor and either the department head or undergraduate coordinator.

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1795Q. Special Topics Lecture

Credits, prerequisites and hours as determined by the Senate Curricula and Courses Committee.

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2010Q. Fundamentals of Algebra and Geometry

Development of the number system with applications to elementary number theory and analytic geometry. May not be counted in any of the major groups described in the Mathematics Departmental listing.

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2011Q. Fundamentals of Algebra and Geometry

A continuation of MATH 2010Q, furthering the treatment of elementary number theory and analytic geometry.

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2110Q. Multivariable Calculus

Two- and three-dimensional vector algebra, calculus of functions of several variables, vector differential calculus, line and surface integrals.

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2141Q. Advanced Calculus I

A rigorous treatment of the mathematics underlying the main results of one-variable calculus. Intended for students with strong interest and ability in mathematics who are already familiar with the computational aspects of basic calculus. May be used in place of MATH 1131Q or 1151Q to fulfill any requirement satisfied by MATH 1131Q or 1151Q.

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2142Q. Advanced Calculus II

A continuation of the rigorous treatment of the mathematics underlying the main results of one variable calculus. Basic properties of vectors and vector valued functions. May be used in place of MATH 1132Q, 1152Q or 2710 to fulfill any requirement satisfied by MATH 1132Q, 1152Q or 2710.

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2143Q. Advanced Calculus III

A rigorous treatment of advanced topics in calculus including vector spaces and their applications in multivariable calculus. May be used in place of MATH 2110Q to fulfill any requirement satisfied by MATH 2110Q.

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2144Q. Advanced Calculus IV

The continuation of the rigorous treatment of advanced topics in multivariable calculus, vector spaces and systems of differential equations. May be used in place of MATH 2210Q or 2410Q to fulfill any requirement satisfied by MATH 2210Q or 2410Q.

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2210Q. Applied Linear Algebra

Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications.

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2360Q. Geometry

Deductive reasoning and the axiomatic method, Euclidean geometry, parallelism, hyperbolic and other non-Euclidean geometries, geometric transformations.

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2410Q. Elementary Differential Equations

Introduction to ordinary differential equations and their applications, linear differential equations, systems of first order linear equations, numerical methods.

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2620. Financial Mathematics I

Fundamental concepts of financial mathematics, with applications in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, duration calculation, asset/liability management, investment income, capital budgeting and valuing contingent cash flows.

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2705W. Technical Writing in Mathematics

An introduction to the communication of mathematics through formal writing.

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2710. Transition to Advanced Mathematics

Basic concepts, principles, and techniques of mathematical proof common to higher mathematics. Logic, set theory, counting principles, mathematical induction, relations, functions. Concepts from abstract algebra and analysis. Students intending to major in mathematics should ordinarily take this course during the third or fourth semester. Students wishing to use MATH 2710 or 2710W as a prerequisite for later MATH courses need to earn a "C" or better.

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2710W. Transition to Advanced Mathematics

Basic concepts, principles, and techniques of mathematical proof common to higher mathematics. Logic, set theory, counting principles, mathematical induction, relations, functions. Concepts from abstract algebra and analysis. Students intending to major in Mathematics should ordinarily take this course or Math 2710 during the third or fourth semester. Students wishing to use MATH 2710 or 2710W as a prerequisite for later MATH courses need to earn a "C" or better.

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2720. History of Mathematics

A historical study of the growth of the various fields of mathematics. This course may not be counted in any of the major groups described in the Mathematics Departmental listing.

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2720W. History of Mathematics

A historical study of the growth of the various fields of mathematics. This course may not be counted in any of the major groups described in the Mathematics Departmental listing.

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2793. Foreign Study

Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure. May count toward the major with consent of the Advisor and either the Department Head or Undergraduate Coordinator.

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2794W. Mathematics Writing Seminar

Contemporary topics in mathematics.

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3094. Undergraduate Seminar

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3146. Introduction to Complex Variables

Functions of a complex variable, integration in the complex plane, conformal mappings.

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3150. Analysis I

Introduction to the theory of functions of one real variable.

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3151. Analysis II

Introduction to the theory of functions of several real variables.

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3160. Probability

Introduction to the theory of probability. Sets and counting, probability axioms, conditional probabilities, random variables, limit theorems.

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3170. Elementary Stochastic Processes

Conditional distributions, discrete and continuous time Markov chains, limit theorems for Markov chains, random walks, Poisson processes, compound and marked Poisson processes, and Brownian motion. Selected applications from actuarial science, biology, engineering, or finance.

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3180. Mathematics for Machine Learning

Applications of elementary linear algebra, probability theory, and multivariate calculus to fundamental algorithms in machine learning. Topics include the theory of orthogonal projection, bilinear forms, and the spectral theorem to multivariate regression and principal component analysis; optimization algorithms such as gradient descent and Newton's method applied to logistic regression; and convex geometry applied to support vector machines. Other topics include Bayesian probability theory and the theory of convolution especially as applied to neural networks. Theory illustrated with computer laboratory exercises.

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3210. Abstract Linear Algebra

Vector spaces and linear transformations over fields.

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3230. Abstract Algebra I

The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields.

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3231. Abstract Algebra II

Topics from ring theory, Galois theory, linear and multilinear algebra, or algebraic geometry.

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3240. Introduction to Number Theory

Euclid's algorithm, modular arithmetic, Diophantine equations, analogies between integers and polynomials, and quadratic reciprocity, with emphasis on developing both conjectures and their proofs.

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3250. Combinatorics

Analysis of combinatorial problems and solution methods. Topics include: Enumeration, generating functions, bijective proofs, sieve methods, recurrence relations, graphs, partially ordered sets, and extremal combinatorics.

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3260. Introduction to Mathematical Logic

Formalization of mathematical theories, elementary model theory with applications to algebra, number theory, and non-standard analysis. Additional topics: Elementary recursion theory and axiomatic set theory. Emphasis on the applications of logic to mathematics rather than the philosophical foundations of logic.

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3265. Applied Mathematical Logic

Applied logic selected from set theory, computability theory, nonclassical logic, and type theory. Topics may include ordinal and cardinal numbers, transfinite recursion, the ZFC axioms, models of computation, undecidable problems, modal logic, intuitionistic logic.

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3330. Elements of Topology

Metric spaces, topological spaces and functions, topological properties, surfaces, elementary topics in geometric topology.

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3370. Differential Geometry

The in-depth study of curves and surfaces in space.

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3410. Differential Equations for Applications

Series solutions of differential equations, Bessel functions, Fourier series, partial differential equations and boundary value problems, nonlinear differential equations.

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3435. Partial Differential Equations

Solution of first and second order partial differential equations with applications to engineering and the sciences.

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3510. Numerical Analysis I

Analysis of numerical methods associated with linear systems, eigenvalues, inverses of matrices, zeros of non-linear functions and polynomials. Roundoff error and computational speed.

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3511. Numerical Analysis II

Approximate integration, difference equations, solution of ordinary and partial differential equations.

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3545. Actuarial Case Studies using SAS

Design, development, testing, and implementation of solutions to problems in actuarial science using SAS.

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3550. Programming for Actuaries

Design, development, testing and implementation of programs to solve actuarial problems using software such as Microsoft Office Excel with Visual Basic.

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3610. Probability Problems

Preparation through problem solving for the probability actuarial examination, which tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk. Recommended prior knowledge: a thorough command of probability, as well as basic concepts in insurance and risk management.

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3615. Financial Mathematics Problems

Preparation for the financial mathematics actuarial examination, which tests a student's knowledge of the theory of interest and financial economics at an introductory level.

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3620. Foundations of Actuarial Science

The foundations of actuarial science, the role of the actuary, external forces that influence actuarial work, and the framework and processes used in actuarial work.

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3630. Long-Term Actuarial Mathematics I

Mathematical foundations of life contingencies and their applications to quantifying risks in other actuarial contexts. Topics include long-term insurance products, survival and longevity models, life tables, life insurance, life annuities, premium calculations, reserves.

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3631. Long-Term Actuarial Mathematics II

Topics include multiple state models, multiple decrements, multiple lives, profit and loss analysis, pension plans and funding, retirement benefits, long-term health and disability.

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3636. Actuarial Statistical Modeling I

Introduction to linear regression models, generalized linear models, and time series models. Case studies are used to demonstrate applications.

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3637. Actuarial Statistical Modeling II

Introduction to principal component analysis, decision tree models, and cluster analysis. Case studies are used to demonstrate applications.

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3639. Actuarial Loss Models

Loss distribution models for claim frequency and severity, aggregate risk models, coverage modifications, risk measures, construction and selection of parametric models, introduction to simulation.

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3640. Short-Term Insurance Ratemaking

Credibility theory, pricing for short-term insurance coverages, reinsurance, experience rating, risk classification, introduction to Bayesian statistics.

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3641. Short-Term Insurance Reserving

Techniques and underlying statistical theory for estimating unpaid claims, use of claims triangles, basic adjustments to data and estimation techniques to account for internal and external environments, estimating recoveries, model adequacy and reasonableness.

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3650. Financial Mathematics II

The continuation of MATH 2620. Measurement of financial risk, the mathematics of capital budgeting, mathematical analysis of financial decisions and capital structure, and option pricing theory.

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3660. Advanced Financial Mathematics

Advanced topics in financial mathematics such as single period, multi-period and continuous time financial models; Black-Scholes formula; interest rate models; and immunization theory.

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3670W. Technical Writing for Actuaries

Students will write a technical report on an advanced topic in actuarial science.

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3710. Introduction to Mathematical Modeling

Theoretical and numerical analysis, using concepts from calculus, differential equations, linear algebra and discrete mathematics, applied to derive and analyze various mathematical models used in other disciplines.

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3710W. Introduction to Mathematical Modeling

Theoretical and numerical analysis, using concepts from calculus, differential equations, linear algebra and discrete mathematics, applied to derive and analyze various mathematical models used in other disciplines.

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3790. Field Study Internship

Consent of the Department Head, Director of the Actuarial Program, or the Undergraduate Coordinator required. Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory.)

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3793. Foreign Study

May be repeated for credit (to a maximum of 15 for MATH 1793 and 3793 together). Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure. May count toward the major with consent of the Advisor and either the Department Head or Undergraduate Coordinator.

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3794. Problem Seminar

Problem sequences selected from algebra, geometry, calculus, combinatorics, and other branches of mathematics, designed to introduce mathematical concepts and to give experience in problem solving.

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3795. Special Topics

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3796W. Senior Thesis in Mathematics

The student should define a general subject area for the thesis before choosing a thesis advisor and seeking consent at the time of registration. The student should submit a written proposal for the senior thesis to the advisor by the end of the semester preceding enrollment for thesis credit.

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3798. Variable Topics

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3799. Independent Study

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3899. Independent Study

Credits and hours by arrangement. Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory).

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4110. Introduction to Modern Analysis

Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, functions of several variables.

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4210. Advanced Abstract Algebra

Group theory, ring theory and modules, and universal mapping properties.

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4310. Introduction to Geometry and Topology

Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.

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