# Contact

**Kevin J. Hastings**

Professor and Chair of Mathematics

2 East South Street, Galesburg, IL 61401-4999

309-341-7438

khasting@knox.edu

# Course Descriptions

MATH 121 Mathematical Ideas (1)An introduction to the history and concepts of elementary mathematics. Topics may include: properties of number systems, geometry, analytic geometry, mathematical modeling, and probability and statistics. Designed for non-majors.

*QSR; QL: MATH 121 cannot simultaneously satisfy both parts of the mathematics proficiency and quantitative literacy requirement; Staff*

MATH 125 Mathematics for Elementary School Educators (1)

A theoretical study of the mathematical concepts taught in elementary school mathematics. Topics include sets, functions, number systems, number theory, statistics, and the role and use of technology.

*Prereq : at least one course in Educational Studies; QL; Staff*

MATH 131 Functions (1)

An introduction to the concept of a function and its graph. Polynomial and rational functions, logarithmic and exponential functions, and trigonometric functions. Examination of the relationship between algebraic and graphical formulations of ideas and concepts.

*QSR; Prereq : 3 years college preparatory mathematics or permission of the instructor; QL; Credit cannot be earned for both MATH 131 and CTL 130; Staff*

MATH 143 Elementary Applied Matrix Algebra (1)

The idea of a matrix, or rectangular array of objects, is surprisingly powerful and pervasive in mathematics and its applications. This course explores the algebraic properties and uses of matrices. Topics include inverses, determinants, systems of linear equations, eigenvalues and eigenvectors, and applications to such areas as network flow, economic input-output analysis, random processes, electric circuits, game theory, and linear optimization.

*Prereq : Three years of high school math and appropriate math placement. Calculus is not required.; Staff*

MATH 145 Applied Calculus (1)

A brief survey of differential and integral calculus from an applied perspective, including some material from multivariate calculus. Mathematical modeling with functions, derivatives, optimization, integration, elementary differential equations, partial derivatives.

*MNS; QSR; Prereq : Appropriate math placement level or MATH 131; QL; Staff*

MATH 151 Calculus I (1)

An introduction to the theory and applications of the differential calculus. Limits, continuity, differentiation, approximation, and optimization.

*MNS; QSR; Prereq : MATH 131 or three years of college preparatory mathematics, including trigonometry, and appropriate placement level; QL; Staff*

MATH 152 Calculus II (1)

A continuation of MATH 151. An introduction to the theory and applications of the integral calculus as well as an introduction to infinite series and parametric equations.

*MNS; QSR; Prereq : MATH 151; QL; Staff*

MATH 175 Discrete Mathematics (1)

A study of discrete mathematical structures. Logic and proof, set theory, relations and functions, ideas of order and equivalence, and graphs.

*MNS; QSR; Prereq : MATH 151 or equivalent, or CS 141 together with MATH 131 or equivalent; QL; Staff*

MATH 180 Combinatorics (1)

The study of problems for which the number of possible solutions is large but finite. Developing, proving, analyzing and applying algorithms to find optimal solutions. Algorithmic graph theory, counting techniques, discrete probability, difference equations.

*Prereq : MATH 151 or equivalent, or CS 141 together with MATH 131 or equivalent; QL; Staff*

MATH 205 Calculus III (1)

An introduction to the calculus of functions of several variables and vector-valued functions. Limits, continuity, differentiation, and multiple integration.

*MNS; QSR; Prereq : MATH 152 or permission of the instructor; QL; D.Schneider;*

MATH 210 Linear Algebra I (1)

A study of the fundamental properties and applications of finite dimensional vector spaces, linear transformations, and matrices. Spanning, independence, bases, inner products, orthogonality, eigenvalues and eigenvectors, diagonalization.

*MNS; Prereq : MATH 152 or permission of the instructor; QL; D.Schneider;*

MATH 211 Linear Algebra II (1)

A continuation of MATH 210. A more abstract study of vector spaces and linear transformations. Spectral and Jordan decomposition theorems. Applications.

*Prereq : MATH 205 and MATH 210; QL; D.Schneider;*

MATH 214 Introduction to Numerical Mathematics (1)

An introduction to elementary numerical methods and their computer implementation. Topics include Newton's method for one and several equations, interpolating functions, approximating polynomials, numerical differentiation and integration, numerical solutions of linear systems of equations, and numerical solutions of differential equations.

*Prereq : MATH 151 or equivalent; QL; A.Leahy;*

MATH 215 Vector Calculus (1)

A study of vector fields and the calculus of vector differential operators (gradient, divergence, curl, Laplacian), potential functions and conservative fields, line and surface integrals, the theorems of Green, Gauss, and Stokes. Applications.

*Prereq : MATH 205; QL; Staff*

MATH 216 Foundations of Geometry (1)

A study of the axiomatic structure and historical development of two-dimensional geometry, with an emphasis on proofs. Incidence geometry, geometry of flat and curved spaces, projective geometry, and Euclidean models for hyperbolic geometry. Historical implications of the existence of non-Euclidean geometries.

*Prereq : MATH 152; QL; Staff*

MATH 217 Number Theory (1)

A study of the properties of the natural numbers. Prime numbers, divisibility, congruences, Diophantine equations, and applications to cryptography.

*Prereq : MATH 152; QL; M.Armon;*

MATH 218 History of Mathematics (1)

A study of the evolution of mathematical ideas from ancient to modern times.

*Prereq : MATH 152; QL; A.Leahy;*

MATH 227 Introductory Financial Mathematics (1)

An introduction to the mathematics of finance including interest, present value, annuities, probability modeling for finance, portfolio optimization, utility theory, and valuation of bonds, futures and options.

*Prereq : MATH 152 or permission of the instructor; K.Hastings;*

MATH 230 Differential Equations (1)

A study of equations involving functions and their derivatives. First and second order equations, linear algebra and systems of linear differential equations, numerical and graphical approximations, and elementary qualitative analysis.

*Prereq : MATH 205; MATH 210 recommended; QL; Staff*

MATH 295 Special Topics (1/2 or 1)

Courses offered occasionally to students in special areas of Mathematics not covered in the usual curriculum.

*Staff*

MATH 300 Mathematical Structures (1)

A rigorous study of the mathematical structures which form the foundation of higher mathematics. Set theory, logic, formal development of the number systems from the natural numbers through the complex numbers, basic algebraic structures (groups, rings and fields), and elementary topological concepts.

*Prereq : MATH 210 or MATH 230; QL; W; Staff*

MATH 311 Scientific Computing (1)

An advanced study of the mathematics of numerical approximation. Error in computation, interpolation, and approximation. Numerical methods of integration, numerical solution to systems of linear equations, ordinary differential equations, and nonlinear equations. Basic notions of computational complexity.

*Prereq : MATH 210 and some programming experience; QL; A.Leahy;*

MATH 313 Topology (1)

A rigorous study of the fundamental ideas of point-set topology. Metric spaces, topological spaces, separation, compactness, connectedness, homeomorphism.

*Prereq : MATH 300; QL; Staff*

MATH 321 Mathematical Statistics I (1)

An advanced study of probability theory. Sample spaces, random variables and their distributions, conditional probability and independence, transformations of random variables.

*Prereq : MATH 205 and MATH 210; QL; W; K.Hastings;*

MATH 322 Mathematical Statistics II (1)

A rigorous study of the theory of statistics with attention to its applications. Point and interval estimation, hypothesis testing, regression and correlation, goodness-of-fit testing, analysis of variance.

*Prereq : MATH 321; QL; K.Hastings;*

MATH 325 Introduction to Operations Research (1)

A rigorous treatment of methods and algorithms for optimization problems, with applications to business and economics and other areas. Networks, linear programming, Markov chains, Poisson processes, queueing theory, dynamic programming.

*Prereq : MATH 321; QL; K.Hastings;*

MATH 327 Advanced Financial Mathematics (1)

Continued study of the key mathematical ideas and techniques of Financial Mathematics. Cox-Ross-Rubinstein model of asset prices, Brownian motion models for continuous time problems, parameter estimation, optimal portfolio consumption problem, exotic options, dynamic programming approach to valuation of derivative assets, Black-Scholes option valuation.

*Prereq : MATH 227 and MATH 321, or permission of the instructor; QL; K.Hastings;*

MATH 331 Analysis I (1)

A rigorous study of the concepts of continuity, differentiation, integration, and convergence in one variable.

*Prereq : MATH 300 or permission of the instructor; QL; W; D.Schneider;*

MATH 332 Analysis II (1)

A continuation of MATH 331. A rigorous study of the concepts of calculus in higher dimensions.

*QL; D.Schneider;*

MATH 333 Complex Analysis (1)

A rigorous study of analytic functions and their properties. The Cauchy-Riemann equations, Cauchy's Theorem, Taylor and Laurent expansions, the calculus of residues, conformal mappings, and harmonic functions.

*Prereq : MATH 331; QL; D.Schneider;*

MATH 341 Abstract Algebra I (1)

A rigorous study of the fundamental notions of abstract algebra. Groups, rings, integral domains, and fields.

*Prereq : MATH 300 or permission of the instructor; QL; W; Staff*

MATH 342 Abstract Algebra II (1)

A continuation of MATH 341. A rigorous study of more advanced topics such as Galois theory, modules and vector spaces.

*QL; Staff*

MATH 360 Research in Mathematics I (.0 or 1/2)

MATH 360-361 is a sequence of two courses in which students engage in guided research of a topic not normally covered elsewhere in the curriculum. Students produce written reports of their work, and do public oral presentations. MATH 361, if taken for 1/2 credit must build on the experience of another course in mathematics numbered 211 or above.

*Prereq : MATH 300; Staff*

MATH 361 Research in Mathematics II (1/2 or 1)

*Prereq : MATH 360 or permission of instructor; Total credit for MATH 360-361 not to exceed 1 credit; O; Staff*

MATH 395 Topics in Advanced Mathematics (1/2 or 1)

Courses offered occasionally to students in special areas of Mathematics not covered in the usual curriculum.

*May be repeated for credit.; Staff*

MATH 399 Seminar in Mathematics (1)

An advanced study of a special topic in mathematics not substantially covered in the regular curriculum. Emphasis on student presentations and independent writing and research. Students submit a major paper and give a public lecture. Recent topics include optimization theory, simulation, and the history of mathematics.

*Prereq : MATH 300 and senior standing or permission of the instructor; O; QL; Staff*

MATH 400 Advanced Studies (1/2 or 1)

See College Honors Program.

*O; Staff*

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