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# Course Descriptions

## Mathematics courses

#### MATH 102: Fund Quantitative Problem Solving

(Fundamentals of Quantitative Problem Solving.) This course focuses on the development of problem-solving skills needed for quantitative courses of study at Lake Forest College. Students will work on problems requiring application of concepts from algebra, probability, and statistics. This 0.50-credit course is graded Pass-Fail with the option to convert to a letter grade. Instructor approval is required. No prerequisites. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)

#### MATH 104: Elem Math from Advanced Standpoint

(Elementary Math from an Advanced Standpoint) This course presents a critical examination of several topics from elementary mathematics. The course stresses three themes: mathematics in the liberal arts, mathematics from a historical perspective, and mathematics as a problem-solving activity. Topics to be covered include college algebra, numeration systems, non-base-10 representations, and elementary number theory including primes and factorizations, rationals as terminating and repeating decimals, irrationals, simple probability experiments, elementary set theory, and mathematical reasoning. Cross-listed as: EDUC 104; No prerequisites. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
cross listed: EDUC 104

#### MATH 105: Elementary Functions

Properties of functions with emphasis on polynomial, exponential, logarithmic, and trigonometric functions. Analytic geometry. (Not open to students who have completed Math 110 with a grade of C- or better.) (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)

#### MATH 108: Calculus Ia

(Calculus Ia: Introduction to Calculus.) The calculus of rational functions of one variable. Limits, continuity, differentiation, and applications; a brief introduction to integration. Related topics in college algebra also are reviewed, including pertinent aspects of functions, polynomials, and rational expressions. This courses is a required skills-building course for students desiring to complete Math 109. (Credit cannot be earned in Math 108 after satisfactory completion of Math 110.) Prerequisite: By placement only. Not open to students who have completed Math 110 with a grade of C- or better. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)

#### MATH 109: Calculus Ib

(Calculus Ib: Transcendental Calculus.) This course is a continuation of Math 108 that further develops the concepts of calculus, such as differentiation and integration, to exponential, logarithm and trigonometric functions. Related topics in exponentiation and analytic geometry are covered as needed. Satisfactory completion of both Math 108 and Math 109 is equivalent to the satisfactory completion of Math 110. (Credit cannot be earned in both Math 109 and Math 110.) Prerequisite: Completion of Math 108 with a grade of C- or better, or permission of the instructor. This course is being offered on a pilot basis for the 2019-2020 academic year. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)

#### MATH 110: Calculus I

The calculus of functions of one variable. Limits, continuity, differentiation, and applications; a brief introduction to integration. Prerequisite: 3.5 years of high school mathematics (to include trigonometry) or Mathematics 105. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 111: Calculus II

The calculus of functions of one variable. Integration, applications of integration, sequences, and series. Prerequisite: Mathematics 110. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 115: Honors Calculus I

Theory and applications of the calculus of functions of one variable, including trigonometric and exponential functions. Limits, continuity, differentiation, integration, and applications. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 116: Honors Calculus II

Continuation of Mathematics 115. Integration and applications, sequences, infinite series. Prerequisite: permission of the instructor. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 150: Intro Probability & Statistics

Designed for students in the social and life sciences. Discrete probability theory, distributions, sampling, correlation, and regression, Chi square and other tests of significance. Emphasis on the use of the computer as a tool and on applications to a variety of disciplines. Not open to students who have taken ECON/BUSN 180 or ECON/BUSN/FIN 130. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 160: Math Methods with Applications

(Mathematical Methods with Applications) Topics from applied mathematics, including equations, inequalities, functions and graphs, and basic properties of logarithmic and exponential functions. Introduction to limits, derivatives and antiderivatives. Applications to business, the social sciences, and the life sciences. (Not open to students who have completed Math 110 with a grade of C- or better.) (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 161: Mathematical Modeling

Mathematical topics as needed to build and solve mathematical models of situations in the life, environmental, and economic sciences. Topics covered include discrete dynamical systems, difference equations, linear, quadratic, and exponential growth models, the logistic model, and examples of chaos in dynamical systems. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 210: Multivariable Calculus

Partial differentiation, the algebra and calculus of vectors, curves and their parameterization, multiple integration, Stokes's and Green's theorem, and applications. Prerequisite: Mathematics 111. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 214: Differential Equations

Differential equation models, analytic solution techniques, qualitative solution concepts, and computer visualization for single equations and systems. Applications of differential equations. Prerequisite: Mathematics 210 or permission of the instructor. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 230: Abstract & Discrete Mathematics

Topics covered include logic and proofs, set theory, relations, cardinal numbers, countable and uncountable sets, permutations and combinations, graph theory, and group theory. Prerequisite: Mathematics 110. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 231: Linear Algebra

Vector spaces, linear independence, linear transformations, matrices, determinants, and applications to geometry. Prerequisite: Mathematics 230 or permission of the instructor. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 240: Intro to Computational Math

(Introduction to Computational Mathematics.) This course provides a survey of computational techniques and methods that are rooted in mathematics and computing. Topics covered include numerical differentiation and integration, numerical solutions to ordinary differential equations, non-linear equations in one variable, and classification methods. Applications of the techniques to "real-life" problems encountered in economics, physics, and/or the life sciences is emphasized. Constructing computer programs to implement the techniques presented also is emphasized. Prerequisites: MATH 110 and CSCI 112. (Under the Forester Fundamental Curriculum, this course meets the Technology requirement.)
cross listed: CSCI 240

#### MATH 250: Intro to Statistical Programming

(Introduction to Statistical Programming.) Introduction to data analysis programming using R. Topics include: data cleaning, data visualization, hypothesis testing, simple and multiple regression, time series analysis, analysis of variance, nonparametrics, and categorical data analysis. No previous programming experience required. Prerequisite: Math 150: Introduction to Probability & Statistics, E/B/F 130: Applied Statistics, PSYC 222: Research Methods & Statistics II, or permission of the instructor.

#### MATH 310: Complex Analysis

Study of functions of one complex variable. Analytic functions, complex integration, Cauchy's theorem, complex power series, and special functions. Applications to other areas of mathematics and to mathematical physics. Prerequisites: Mathematics 210 and 230 or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 311: Introduction Real Analysis

A rigorous course covering the following introductory real analysis topics: axioms for the real numbers, sequences, boundedness, limits, monotone functions, continuity, uniform continuity, Cauchy criterion for convergence, cluster points, compactness, differentiability, integration, and infinite series. Prerequisites: Mathematics 210 and 230. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 323: Cryptography

An introduction to cryptology and cryptanalysis, the making of codes and the breaking of codes. History and basic concepts. Classical ciphers and attacks on classical ciphers. One-time Pad. Modern ciphers including DES, AES. Public key ciphers including RSA and Diffie-Hellman. Digital signatures. Additional topics may include Elliptic Curve systems, knapsack systems, and other cryptographic systems. Prerequisites: Mathematics 230 and Computer Science 212, or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
cross listed: CSCI 323

#### MATH 329: Number Theory

Mathematical induction, divisibility properties of integers, prime numbers, and congruences. Prerequisite: Mathematics 230 or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 330: Abstract Algebra

A study of algebraic structures with emphasis on groups, rings, and fields. Prerequisite: Mathematics 230. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 334: Theory of Computation

This course covers fundamental ideas in the theory of computation, including formal languages, computability, complexity, and reducibility among computational problems. Topics include formal languages, finite state automata, Kleene's theorem, formal grammars, pushdown automata, context-free languages, Turing machines, computability, Church's Thesis, decidability, unsolvability, and NP- completeness. Prerequisites: CSCI 212 and Mathematics 230. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
cross listed: CSCI 334

#### MATH 340: Geometry

Selected topics from affine, Euclidean, non-Euclidean, projective, and differential geometry. Prerequisite: Mathematics 230 or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 350: Mathematical Probability

Discrete and continuous probability. Distributions, the law of large numbers, the central limit theorem, random variables, and generating functions. Prerequisites: Mathematics 210 and 230 or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 360: Mathematical Modeling

Introduction to the process and techniques of modeling physical problems, including computing strategies and analysis of results. Python programming will be emphasized. Numerical methods covered include solutions to linear and non-linear equations, solutions to ordinary and partial differential equations, finite elements, linear programming, and optimization algorithms. Prerequistes: MATH 210 and CSCI 112. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
cross listed: CSCI 360

#### MATH 375: Combinatorics & Graph Theory

Enumeration techniques with emphasis on permutations and combinations, generating functions, recurrence relations, inclusion and exclusion, and the pigeonhole principle. Graph theory with emphasis on trees, circuits, cut sets, planar graphs, chromatic numbers, and transportation networks. Additional topics from designs with emphasis on Latin squares, finite projective and affine geometries, block designs, and design of experiments. Prerequisite: Mathematics 230. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
cross listed: CSCI 375

#### MATH 410: Topology

Point set topology. Such topics as topological spaces, separation axioms, covering properties, metrization, convergence and completeness, and homotopy theory. Prerequisite: Mathematics 311. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 411: Advanced Topics in Analysis

Introductory notions of functional analysis. Banach spaces, integration and measure, Hilbert spaces, and commutative Banach algebras. Prerequisite: Mathematics 311. (Under the Forester Fundamental Curriculum, this course meets the Senior Studies requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

#### MATH 430: Advanced Topics in Algebra

Additional topics in modern or linear algebra such as field extensions, Galois Theory, group conjugacy, modules, eigenvalue theory, dual spaces, and unitary spaces. Prerequisite: Mathematics 330 or permission of the instructor. (Under the Forester Fundamental Curriculum, this course meets the Senior Studies requirement.)

#### MATH 450: Mathematical Statistics

A mathematical study of such topics as estimation of parameters, confidence intervals and tests of hypotheses, decision theory, regression, analysis of variance, and nonparametric methods. Prerequisite: Mathematics 350. (Under the Forester Fundamental Curriculum, this course meets the Senior Studies requirement.)

#### MATH 499: Great Theorems of Mathematics

Seminar course to introduce students to various masterpieces in the development of mathematics. Some of the most historically important proofs and ingenious logical arguments from mathematics will be presented and discussed. An emphasis will be placed on the interconnectedness among various subject areas within mathematics. Prerequisite: permission of the instructor.