# Mathematics Courses

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#### MATH-110 Great Ideas In Mathematics

The beauty and significance of mathematics in the history of human thought. Topics include primes, the pigeonhole principle, the Fibonacci sequence, infinity, chaos and fractals. Not for General Science majors. Prerequisites: high school algebra I and geometry, or equivalent. Offered spring of even-numbered years. 3 credits. (QR)

#### MATH-120 Intro To Game Theory

Topics in economic game theory including two- person zero-sum games, Prisoner's Dilemma, n-person competitive and cooperative games. Focus on concepts of strategy, fairness, cooperation and defection, utility and individual rationality. The social impact of individual choices. Prerequisites: High school algebra I and geometry, or equivalent. Offered fall of even-numbered years. 3 credits. (QR)

#### MATH-125 Introduction To Voting Theory

Study of voting and elections from a mathematical perspective; examination of preferential voting systems with focus on axioms of fairness; weighted voting systems and indices of power; methods of apportionment, paradoxes, and the Electoral College. Prerequisites: High school algebra and geometry or equivalent. Offered fall of odd-numbered years. 3 credits. (QR)

#### MATH-130 Problem Solving

Mathematical problem solving; understanding the problem, devising a plan to solve the problem, implementing the plan, verifying and communicating the solution. Specific problem strategies and types of problems for which they are appropriate. Emphasis on communication, collaboration and problem-solving strategies. Prerequisites: High school algebra I and geometry, or equivalent. Offered spring of odd-numbered years. 3 credits. (QR)

#### MATH-135 Mathematics For Elementary Teacher I

The mathematics of the elementary school. Problem solving, sets and logic, number and numeration systems, whole number operations and their properties, patterns among natural numbers, the art of guessing, fractions, decimals, ratios and portions, integers, rational and irrational numbers, and the use of calculators. Prerequisite: 105 or equivalent. 4 credits. (QR)

#### MATH-136 Math For Elementary Teachers II Teachers II

A continuation of 135. Collection and treatment of data, concepts of probability, measurement, spatial concepts including one, two, and three dimensional shapes, congruence, similarity, transformations, graphic and computers including the use of Logo. Prerequisite: 135 or consent of instructor. 4 credits.

#### MATH-140 Introduction To Statistics

An introduction to probability and statistics including methods of summarizing and describing data, basics of probability, distribution of random variables and probability distributions including the normal curve, inferential statistics including hypothesis testing and decision making, linear regression and correlation. Additional topics may include chi-square analysis and analysis of variance. Prerequisite: 105, or high school algebra I and II and geometry or equivalent. 3 credits. (QR)

#### MATH-150 Precalculus

Topics in algebra and trigonometry beyond those covered in the second course in high school algebra. Emphasis on concepts, structures and technical competence. Solutions of algebraic equations and inequalities; functions and graphs; exponential, logarithmic, and trigonometric functions; elementary plane analytic geometry. Prerequisite: 105, or high school algebra I and II and geometry, or equivalent. 5 credits.

#### MATH-160 Finite Mathematics With Calculus

Review of algebra including equations, inequalities, functions, graphs, logarithms and exponentials. Topics in finite mathematics including matrix algebra and linear programming. Introduction to differential calculus and use in optimization. Applications in business, economics and the social sciences. Prerequisite: 105 or equivalent. 5 credits.

#### MATH-170 Calculus I

Differential and integral calculus of real functions of one variable. Differentiation, the chain rule, the mean-value theorem, the fundamental theorem, limits and continuity, curve sketching. Integration by substitution. Application of the derivative and integral to physics and geometry. Prerequisite: 150 or equivalent. 5 credits.

#### MATH-175 Calculus II

A continuation of Calculus I to include further techniques of integration, Taylor approximations, sequences and series. Plane analytic geometry, parametric equations, including polar form. Prerequisite: 170 or equivalent with a grade of C- or better. 3 credits.

#### MATH-200 Vector Calculus

Functions of several variables; differentiability and continuity; arc length and differential geometry; Taylor's formula; extrema and Lagrange multipliers; multiple integration, line and surface integrals; the theorems of Green, Gauss and Stokes. Prerequisite: 175 or equivalent. 5 credits.

#### MATH-210 Ordinary Differential Equations

First-order equations, including separation of variables and integrating factors; second-order linear equations, including nonhomogeneous techniques, Laplace transforms and power series methods; linear systems, including eigenvalue methods and matrix exponentials; applications to mechanics, physics, chemistry, biology and economics. Prerequisite: 175 or equivalent. Offered spring. 4 credits. (QR)

#### MATH-220 Introduction To Proofs

Fundamental concepts in abstract mathematics with an emphasis on learning to write mathematical proofs. Topics include logic, sets, relations, functions, proof by contradiction, proof by contrapositive, and mathematical induction. Prerequisite: 170 or equivalent with grade of C- or better. Offered January term. 3 credits.

#### MATH-230 Discrete Mathematics

Topics in the general area of discrete mathematical structures including sets, logic, relations, functions, induction, matrices, basic enumeration, graphs, and Boolean algebra. Prerequisite: 170 or equivalent with grade of C- or better. Offered fall. 4 credits.

#### MATH-250 Linear Algebra

Matrix theory and linear algebra, including real and complex vector spaces, linear transformations and their matrices, systems of linear equations, determinants, similarity, eigenvalues, symmetric and Hermitian matrices. Prerequisite: 170 or equivalent with grade of C- or better. 4 credits.

#### MATH-280 Mathematical Modeling Experience

Participation in the Mathematical Contest in Modeling sponsored by the Consortium for Mathematics and its Applications. Experience solving real world problems using mathematical methods. Formal presentation of project results. May be repeated for credit. Prerequisite: consent of instructor. Offered spring. 1 credit.

#### MATH-290 History of Mathematics

Topics in the development of mathematics from ancient times to present. Prerequisites: 175 and INQS 125 or consent of instructor. Offered spring of even-numbered years. 3 credits.

#### MATH-310 Nonlinear Ode's & Dynamic Systems

Nonlinear differential equations from a dynamical systems approach. Scalar autonomous equations; elementary bifurcations; linear systems and canonical forms; planar autonomous systems; stability near equilibria including Liapunov functions; periodic orbits and the Poincare-Bendixson theorem; Lorenz equations, chaos and strange attractors; one-dimensional maps including the logistical map. Prerequisites: 200 and 210 or consent of instructor. Offered fall of even-numbered years. 3 credits. (QR)

#### MATH-320 Higher Geometry

Geometry as a body of theory developed logically from a given set of postulates. Euclid's definitions and postulates; independence, consistency, and completeness; finite axiomatic systems; modern incidence results of the circle and triangle; duality in synthetic projective geometry; Cartesian and homogeneous coordinates; transformations of the plane. Prerequisite: 250 (may be taken concurrently). Offered fall of even-numbered years. 4 credits.

#### MATH-330 Combinatorics

Combinatorical theory with focus on techniques of enumeration. Topics include generating functions, recurrence relations, inclusion-exclusion, pigeonhole principle. Advanced topics selected from posets, lattices, Polya counting, difference sequences, Stirling numbers, and Catalan numbers. Prerequisites: 175 and at least one of 220, 230, or 250. Offered spring of odd-numbered years. 3 credits.

#### MATH-340 Probability and Statistics I

Discrete and continuous random variables; descriptive statistics of a single random variable; the Central Limit Theorem; applications of confidence intervals and hypothesis testing; linear regression. Prerequisites: 175. Offered fall. 4 credits. (QR)

#### MATH-350 Number Theory

Properties of the integers. Divisibility, prime numbers, congruence. Chinese Remainder Theorem, Wilson's Theorem, Euler's Theorem. Emphasis on writing proofs in the context of number theory; mathematical induction. Prerequisite: 220, 230 or 250. Offered spring of odd-numbered years. 3 credits.

#### MATH-360 Operations Research

Mathematical methods of examining allocation problems; formulation and solution of linear programming problems, simplex method, and duality; additional topics may include game theory, queuing models, dynamic programming, and/or Markov chains. Prerequisites: 200, 250. Offered spring of odd-numbered years. 3 credits. (QR)

#### MATH-370 Elementary Analysis

The analysis of real-valued functions; sequences including Cauchy sequences; limits and continuity including uniform continuity; differentiation, the mean value theorem and Taylor's Theorem; the Riemann integral and the fundamental theorem of calculus. Prerequisites: 175, at least one of 220, 230, or 250. 3 credits.

#### MATH-380 Numerical Analysis

Numerical analysis involving mathematical and statistical methods, use of interactive mathematical software to solve such problems. Topics include: numerical solution of non-linear equations, numerical solution of systems of equations, numerical differentiation and integration, numerical solution of ordinary differential equations, interpolation, curve fitting, analysis of errors. Prerequisites: 200, and 250 (may be taken concurrently). Offered spring of odd-numbered years. 4 credits.

#### MATH-400 Topics In Mathematics

Selected topics not regularly offered at Linfield. 1-5 credits.

#### MATH-410 Partial Differential Equations

Fourier series and the methods of separation of variables; Sturm-Liouville problems; Green's functions; the method of characteristics; Laplace, heat and wave equations, and selected applications. Prerequisites: 200, 210. Offered fall of odd-numbered years. 3 credits.

#### MATH-420 Topology

Basic topics in point set topology. Product, quotient and subspace topologies; metric spaces; closed sets and limit points; connectedness; compactness; the separation axioms; introduction to fundamental group and covering spaces. Prerequisites: 200, and at least one of 220, 230, or 250. Strongly recommended: 370. Offered fall of odd-numbered years. 3 credits.

#### MATH-430 Graph Theory

Topics in graph theory including trees, bipartite graphs, Eulerian and Hamiltonian graphs, matchings, connectivity, coloring, planar graphs. Advanced topics selected from Ramsey theory, pebbling, competitive coloring, and matroids. Prerequisite: 220, 230, or 250. Offered spring of even-numbered years. 3 credits.

#### MATH-440 Probability & Statistics II

Multivariate probability distributions; functions of random variables; point estimators; maximum likelihood estimators; theory of hypothesis testing and power; method of least squares. Prerequisite: 200, 340. Offered spring of even-numbered years. 3 credits.

#### MATH-450 Abstract Algebra

Basic algebraic structures; groups, rings, and fields. Cosets, normal subgroups, factor groups, ideals, factor rings, polynomial rings. Homomorphisms and isomorphisms. Prerequisite: 220, 230, or 250. Offered fall of odd-numbered years. 4 credits.

#### MATH-460 Complex Analysis

Complex numbers and functions; the complex derivative; complex integration; Taylor and Laurent series; residue theory; conformal mapping. Selected applications. Prerequisites: 200, 370. Offered spring of odd-numbered years. 4 credits.

#### MATH-470 Real Analysis

Infinite Series of Real Numbers; Infinite Series of Functions including Power Series and Analytic Functions; Topology of Euclidean Spaces; Differentiability on R^n; Riemann Integration on R^n; Measurable sets and functions; Introduction to Lebesgue integration and convergence theorems. Prerequisites: 200, 250, and 370. Offered spring of even-numbered years. 4 credits.

#### MATH-480 Independent Study

Study of selected topics under an instructor's guidance. For advanced mathematics majors with a high degree of self-reliance. Periodic written and oral reports and, in most cases, a comprehensive final paper. 1-5 credits.

#### MATH-485 Senior Seminar

Department capstone course. Examination of the nature of mathematics and its role within the liberal arts. Focus on reading current mathematics, writing a survey article, and presenting results. Prerequisites: 370 and senior standing, or consent of instructor. Offered spring. 3 credits. (MWI)

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