Mathematics Degrees

The analytical and problem-solving skills cultivated by students majoring in mathematics are both versatile and highly valued in industry, government, and education. The bachelor of science degree program in mathematics is designed to prepare students to (1) attend professional and graduate school in mathematics, (2) teach mathematics in secondary school, or (3) seek employment in mathematical related fields in the public and private sectors. Students majoring in mathematics may arrange their course work according to their interests. There are two tracks of study: Applied Mathematics, which offers concentrations in Operations Research and Statistics, and Mathematics Education.

The Applied Mathematics track provides excellent preparation for graduate study or careers where mathematical ideas and techniques are used to model and solve real world problems. The Mathematical Education track is designed for students interested in teaching high school level mathematics. Regardless of which track is chosen, all students majoring in mathematics must satisfy a common upper level core. Coursework beyond the upper level core is taken according to the track and concentration chosen.

Macon State’s bachelor of science in mathematics is designed to meet growing occupational demands in two areas.

The applied mathematics major prepares students to enter professions requiring foundations in analytical training and qualify them for positions as statisticians, actuaries, operations research analysts, cost estimators, science technicians and similar careers . In Central Georgia, Robins Air Force and the aerospace industry have extensive needs for graduates with a strong mathematics background.

The mathematics education major prepares students to become high school teachers and help address shortages of secondary mathematics educators in Central Georgia. However, the degree differs from many traditional secondary education programs in that students who complete the requirements earn a bachelor’s degree in math, rather than a degree in education. Students take 24 semester hours of education classes that will make them eligible to become certified to teach, but they take more mathematics classes than are generally offered in traditional mathematics education degree programs.

MATH-1410 – College Algebra
4.00 credit hours

Prerequisite: MATH-1000 with grade C or better, or an equivalent college or high school course, or an acceptable score on a placement or prerequisite exam

(formerly MATH-1420) No credit after MATH-1420, MATH-1450, MATH-1460. MATH-1410 is one of two courses whose combined content parallels that of MATH-1460 and includes functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, and special topics. Calculators are used throughout the course. (4 contact hrs) MATH-1430 – College Trigonometry
3.00 credit hours

Prerequisite: MATH-1410 or MATH-1420 with grade C or better, or a college mathematics course comparable to MATH-1410 with grade C or better, or an equivalent high school college prep course with grade C or better, or an acceptable score on a placement exam

(formerly MTH 143) No credit after MATH-1450 or MATH-1460. This course presents algebraic and geometric review of the essentials for trigonometry; triangle trigonometry, analytic trigonometry, trigonometric identities, trigonometric functions, inverse trigonometric functions, vectors, polar coordinates, polar graphs, complex numbers in rectangular and polar form, and DeMoivre’s theorem. Calculators are used throughout the course. (3 contact hrs) MATH-1460 – Precalculus
4.00 credit hours

Prerequisite: MATH-1000 with grade B or better, or the equivalent college or high school course, or an acceptable score on the placement exam

(formerly MATH-1450) No credit after MATH-1430. This course takes an analytical approach to the elementary mathematical functions and includes equations; inequalities; conic sections; relations; function properties and graphs; polynomials; rational, exponential, logarithmic, and trigonometric functions; trigonometric identities; and the theory of equations. Calculators are used throughout the course. (4 contact hrs) MATH-1760 – Analytic Geometry & Calculus 1
4.00 credit hours

Prerequisite: MATH-1430 or MATH-1460 with grade C or better, or equivalent college course or equivalent high school course, or an acceptable score on a placement or prerequisite exam

(formerly MTH 176) MATH-1760 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes limits; continuity; differentiation of algebraic and transcendental functions including trigonometric, logarithmic and exponential base-e functions; mean-value theorem; applications of the derivative to curve sketching; optimization; related rates; conics; differentials; antidifferentiation of algebraic and trigonometric functions; the definite integral; the fundamental theorem of calculus; application of the definite integral to areas; and numerical integration. (4 contact hrs) MATH-1770 – Analytic Geometry & Calculus 2
4.00 credit hours

Prerequisite: Grade C or better in MATH-1760 or equivalent college course

(formerly MTH 177) MATH-1770 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes volumes of solids of revolution; differentiation and integration of trigonometric, inverse trigonometric, logarithmic, exponential, and hyperbolic functions; integration techniques; L’Hopital’s Rule, indeterminate forms and improper integrals; sequences and series; Taylor series; Maclaurin series; and differentiation and integration of power series. (4 contact hrs) MATH-2000 – Introduction to Linear Algebra
3.00 credit hours

Prerequisite: Grade C or better in MATH-1760 or equivalent college course, or by exam

(formerly MTH 200) Systems of linear equations. The algebra of matrices. Determinants and their applications. The theory of vector spaces, with emphasis on Euclidean n-space. Linear transformations and their matrix representations. Eigenvalues and eigenvectors. Similar matrices. Symmetric matrices, the spectral theorem and applications. (3 contact hrs) MATH-2200 – Discrete Mathematics
4.00 credit hours
Prerequisite: MATH-1410 with grade C or better, or equivalent college course or equivalent high school course, or an acceptable score on placement exam or prerequisite exam
(formerly MTH 220) MATH-2200 is an introduction to logic; circuits; graphs; trees; matrices; algorithms; combinatorics and relations within the context of applications to computer science. (4 contact hrs) MATH-2760 – Analytic Geometry & Calculus 3
4.00 credit hours
Prerequisite: Grade C or better in MATH-1770 or equivalent college course
(formerly MTH 276) MATH-2760 is part of a sequence of courses required for most engineering, science, and mathematics majors and includes concepts and procedures from vector algebra, vector calculus, quadric surfaces, calculus of functions of two and three variables, multiple integrals, and line integrals. (4 contact hrs) MATH-2770 – Differential Equations
4.00 credit hours
Prerequisite: Grade C or better in MATH-2000 and MATH-2760 or equivalent college course
(formerly MTH 277) MATH-2770 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes first order differential equations and their applications, higher order differential equations and their applications, differential operators, the Laplace Transform, systems of linear differential equations, series solutions of differential equations, and numerical methods for solving differential equations. (4 contact hrs) MATH-2902 – Directed Study
2.00 credit hours
Prerequisite: Approval of directed study agreement.
Under the direction of an appropriate faculty member, students may pursue studies related to their academic interests on an independent basis. (2 contact hrs) MATH-2903 – Directed Study
3.00 credit hours
Prerequisite: Approval of directed study agreement.
Under the direction of an appropriate faculty member, students may pursue studies related to their academic interests on an independent basis. (3 contact hrs) MATH-2911 – Supplemental Instruction for MATH-0070
0.00 credit hours
Prerequisite: None
Corequisite: MATH-0070
This course provides additional support and instruction on topics covered in MATH-0070. This course is graded on a pass/fail basis. Pass/fail grades are not included in GPA calculations. (1 contact hr)

MATH-0050 – Fundamentals of Mathematics
3.00 credit hours

Prerequisite: None

(formerly MTH 005) MATH-0050 is a refresher course in the concepts and skills of arithmetic and includes integers, fractions, decimals, percent, measurement, and an introduction to algebra. (3 contact hrs) MATH-0070 – Beginning Algebra
3.00 credit hours

Prerequisite: Grade C or better in MATH-0050 or an equivalent college or high school course, or an acceptable score on a placement or prerequisite exam

(formerly MTH 007) A course in beginning algebra dealing with an introduction to sets of real numbers. Addition, subtraction, multiplication, division, and factoring of polynomials. Integral exponents. Linear equations and inequalities in one variable. Linear equations and systems of linear equations in two variables. Roots and radicals, rational expressions and equations. (3 contact hrs) MATH-1000 – Intermediate Algebra
4.00 credit hours

Prerequisite: Grade C or better in MATH-0070 or an equivalent college or high school course, or an acceptable score on a placement exam or prerequisite exam

(formerly MTH 100) (3 credit hours prior to Fall 1990) MATH-1000 is an additional course in algebra and includes linear equations and inequalities in one and two variables; systems of linear equations in two and three variables; expressions and equations containing quadratic, rational, radical, exponential, and logarithmic terms; rational and quadratic inequalities; complex numbers; graphs of lines, parabolas and circles; and an introduction to functions and functional notation. A scientific calculator is required. (4 contact hrs) MATH-1280 – Mathematics for Education 1
4.00 credit hours

Prerequisite: Grade C or better in MATH-1000 or a college mathematics course comparable to MATH-1000 or an equivalent high school college prep course or an acceptable score on a placement exam

(formerly MATH-1260) MATH-1280 is the first course in a two-course sequence for elementary education students and includes technology; sets; relations; functions; logic; mathematical systems; systems of numeration; natural numbers, integers, rational, and real numbers; prime numbers; and greatest common factor; and least common multiple. (4 contact hrs) MATH-1290 – Mathematics for Education 2
4.00 credit hours

Prerequisite: Grade C or better in MATH-1280 or an equivalent college course

(formerly MATH-1270) MATH-1290 is the second of a two-course sequence for elementary education students and includes non-metric geometry, metric geometry, coordinate geometry, the metric system, probability, and statistics. (4 contact hrs) MATH-1340 – Statistics
4.00 credit hours

Prerequisite: Grade C or better in MATH-1000 or equivalent college or high school course, or an acceptable score on a placement exam or prerequisite exam

(formerly MATH-1330) MATH-1340 is for students in those fields where statistical investigations are necessary and includes description of sample data, probability, frequency distributions, sampling, confidence intervals, estimation, testing hypothesis, correlation, chi-square distributions, and nonparametric tests. (4 contact hrs) MATH-1360 – Finite Mathematics
4.00 credit hours

Prerequisite: Grade C or better in MATH-1000 or equivalent college or high school course, or an acceptable score on a placement exam or prerequisite exam

(formerly MTH 136) MATH-1360 is the first of two mathematics courses for students majoring in the areas of business, social science, or life science and includes applications of linear, quadratic, polynomial, exponential, and logarithmic functions; systems of linear equations and inequalities; algebra of matrices and linear programming; elements of probability theory; applications of probability. (4 contact hrs) MATH-1370 – Calculus for Business & Social Sciences
4.00 credit hours

Prerequisite: MATH-1360 or MATH-1410 or MATH-1460 with grade C or better, or equivalent college or high school course, or an acceptable score on a placement or prerequisite exam

(formerly MTH 137) MATH-1370 is the second of two mathematic courses for students majoring in the areas of business, social science, or life science and includes differentiation techniques, optimization, applications of differentiation, the definite integral, finding areas using integration, and applications of integration. (4 contact hrs)

484 INTRODUCTION TO ARTIFICIAL INTELLIGENCE (Same as Cognitive and Neuroscience Studies 484)
An introduction to the basic principles and techniques of artificial intelligence. Topics will include specific AI techniques, a range of application areas, and connections between AI and other areas of study (i.e., philosophy, psychology). Techniques may include heuristic search, automated reasoning, machine learning, deliberative planning and behavior-based agent control. Application areas include robotics, games, knowledge representation, logic, perception, and natural language processing. Prerequisites: Computer Science 221, or consent of instructor. Note that the Cognitive and Neuroscience Studies 484 prerequisites are different. Alternate fall semesters; next offered Fall 2008. (4 credits)

488 SENIOR SEMINAR IN COMPUTER SCIENCE
Advanced topics in specialized areas of computer science. The course will be taught as a seminar and will involve discussion of original research articles, student projects, and oral presentations. When the course is offered, the topic and prerequisites for that semester will be announced and posted prior to registration. (4 credits)

490 SENIOR CAPSTONE SEMINAR
Working with their capstone supervisor, seminar coordinators, and other faculty, students will discuss their capstone project, make presentations of their progress, critique the work of other students, and participate in the activities of the seminar. These activities will include instruction and discussion of strategies for research, writing, and presentation. The scheduled times will include both group meetings with other seminar participants as well as individually arranged meetings with the student’s capstone supervisor. Every semester. S/NC grading only. (1 credit)

604 TUTORIAL
Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of computer science not available through the regular offerings. Every semester. (1–4 credits)

614 INDEPENDENT PROJECT
Individual project including library research, conferences with instructor, oral and written reports on independent work in computer science. Subject matter may complement but not duplicate material covered in regular courses. Arrangements must be made with a department member prior to registration. Prerequisite: departmental approval. Every semester. (1–4 credits)

624 INTERNSHIP
Available to junior and senior students with declared majors in computer science. Arrangements must be made prior to registration, and departmental approval and supervision is required. For additional information about internships and how they are administered, refer to the section of the catalog entitled Individualized Learning. Internships are offered only as S/D/NC grading option. Every semester. (1–4 credits)

634 PRECEPTORSHIP
Available to junior and senior students with declared majors in computer science. Arrangements must be made prior to registration. Departmental approval and supervision required. Every semester. (1–4 credits)

644 HONORS INDEPENDENT
Independent research, writing, or other preparation leading to the culmination of the senior honors project. Every semester. (1–4 credits)

221 ALGORITHM DESIGN AND ANALYSIS
An in-depth introduction to the design and analysis of algorithms. Topics may include algorithmic paradigms and structures, including recursion, divide and conquer, dynamic programming, greedy methods, branch and bound, randomized, probabilistic, and parallel algorithms, non-determinism and NP completeness. Applications to searching and sorting, graphs and optimization, geometric algorithms, and transforms. Prerequisites: Computer Science 124, Mathematics 136, or consent of instructor. Every fall. (4 credits)

225 SOFTWARE DESIGN AND DEVELOPMENT
This course builds upon the software design foundation started in Computer Science 124. Students will design and implement medium-sized software projects using modern software design principles such as design patterns, refactoring, fault tolerance, stream-based programming, and exception handling. The concept of a distributed computing system will be introduced, and students will develop multithreaded and networked applications using currently available software libraries. Advanced graphical user interface methods will be studied with an emphasis on appropriate human-computer interaction techniques. Students will use operating systems services and be introduced to methods of evaluating the performance of their software. Prerequisite: Computer Science 124, or consent of instructor. Every fall. (4 credits)

240 COMPUTER SYSTEMS ORGANIZATION
This course familiarizes the student with the internal design and organization of computers. Topics include number systems, internal data representations, logic design, microarchitectures, the functional units of a computer system, memory, processor, and input/output structures, instruction sets and assembly language, addressing techniques, system software, and non-traditional computer architectures. Prerequisite: Computer Science 120, 121, or 123, or consent of instructor. Every spring. (4 credits)

261 THEORY OF COMPUTATION (Same as Mathematics 361)
Investigation of the theoretical foundations of computer science as embodied in formal models of computation, including finite state automata, regular expressions, formal languages, and Turing machines. Properties of computation, including computability, unsolvability, and the theory of computational complexity. Prerequisite: Computer Science 124 and Mathematics 136, or consent of instructor. Every spring. (4 credits)

325 PRINCIPLES OF COMPILER DESIGN
The principles, techniques, and theory underlying the design of compilers and language translators. Topics will include lexical analysis, symbol tables, a variety of parsing algorithms, automated scanner and parser generation, representation and generation of intermediate code, machine code generation, and code optimization. Prerequisites: Computer Science 240 and 261, or consent of instructor. Offered alternate fall semesters; next offered Fall 2009. (4 credits)

340 DIGITAL ELECTRONICS (Same as Physics and Astronomy 340)
A survey of fundamental ideas and methods used in the design and construction of digital electronic circuits such as computers. Emphasis will be on applying the theoretical aspects of digital design to the actual construction of circuits in the laboratory. Topics to be covered include basic circuit theory, transistor physics, logic families (TTL, CMOS), Boolean logic principles, combinatorial design techniques, sequential logic techniques, memory circuits and timing, and applications to microprocessor and computer design. Three lectures and one three-hour laboratory per week. Prerequisite: Mathematics 137 and permission of instructor. Offered alternate spring semesters; next offered Spring 2009. (4 credits)

342 OPERATING SYSTEMS AND COMPUTER ARCHITECTURE
The basic principles related to the design and architecture of operating systems. Concepts to be discussed include sequential and concurrent processes, synchronization and mutual exclusion, processor scheduling, time-sharing, multiprogramming, multitasking, and parallel processing. Memory management techniques. File system design. Security and protection systems. Performance evaluation. Prerequisite: Computer Science 240, or consent of instructor. Offered alternate spring semesters; next offered Spring 2009. (4 credits)

343 DESIGN OF COMPUTER NETWORKS
This course investigates basic principles for designing and implementing both local area networks (LANs) and wide-area networks (WAN). It will look at 1) physical layer protocols, including transmission media, analog vs. digital communications, and interface design, 2) data link layer protocols, for point-to-point and contention-based message passing, 3) network layer protocols, for routing, congestion control, and inter-network communication, and 4) transport protocols, for creating error-free end-to-end channels. Each of these concepts will be illustrated using actual communication protocols such as the Ethernet and TCP/IP. The course will also take a brief look at higher level application issues including security (e.g. encryption, authentication), network management, name servers, and multimedia protocols such as JPEG and MPEG. Prerequisites: Computer Science 240 and 221, or consent of instructor. Offered alternate fall semesters; next offered Fall 2009. (4 credits)

346 INTERNET COMPUTING
This course will investigate the latest technology available for building web applications with dynamic content. It will look at all stages in the web application design process, including: 1) client applications, 2) web applications that service client requests, 3) application servers that manage requests for information, update data, and serve client applets, and 4) the database management system that holds the data. The course will be programming-intensive using aspects of the Java language available for designing and implementing Internet applications. The format of the course will be mainly laboratory-based sessions where you learn to build these four components of a web application, supported by lectures and discussions. Students will research particular topics and present their findings during these discussion sessions. The course will also investigate the usability of designs from a human factors standpoint and discuss privacy and other social consequences of this technology. Prerequisite: Computer Science 225, or consent of instructor. Offered alternate fall semesters; next offered Fall 2008. (4 credits)

365 SCIENTIFIC COMPUTATION (Same as Mathematics 365)
Techniques and algorithms for computational solutions to scientific problems with applications to diverse disciplines. Topics include: numerical integration; root finding; interpolation, splines, and Bezier curves; statistical function estimation; modeling via simulation and Monte Carlo techniques; optimization; transforms; symbolic computing; controlling numerical error. Prerequisites: Computer Science 121 or 123, Math 137. Linear Algebra (Math 236) strongly recommended. Every spring. (4 credits)

369 DISCRETE APPLIED MATHEMATICS (Same as Mathematics 469)
Topics in applied mathematics chosen from: cryptography; complexity theory and algorithms; integer programming; combinatorial optimization; computational number theory; applications of geometry to tilings, packings, and crystallography; applied algebra. Prerequisites: Math 236 and 379 and Computer Science 121 or 123. Alternate fall semesters; next offered Fall 2008. (4 credits)

425 PROGRAMMING LANGUAGE CONCEPTS
Introduction to programming language concepts, including issues of design, specification, representation, and implementation across a range of language types (procedural, object-oriented, functional, declarative, and parallel). Specific topics will include models of computation and their influence on language design, syntax, semantics and abstract interpretation, language structures, type theories, and program transformation methods, such as interpretation, compilation, partial evaluation, and graph reduction. Prerequisites: Computer Science 221 and 261, or consent of instructor. (4 credits)

445 PARALLEL PROCESSING
An introduction to the field of parallel processing and its three major subareas of parallel architectures, parallel languages, and parallel algorithms. Topics include SIMD and MIMD systems, private memory and shared memory designs, dataflow architectures; issues in parallel language design such as process creation and management, message passing, synchronization, and deadlock; the design and formal analysis of parallel algorithms in areas such as sorting, searching, numerical methods, and graph theory. Students will design and implement software for an actual parallel processing system. Prerequisites: Computer Science 240 and 221, or consent of instructor. (4 credits)

480 INTRODUCTION TO DATABASE MANAGEMENT SYSTEMS
This course will introduce students to the design, implementation, and analysis of databases stored in database management systems (DBMS). Topics include implementation-neutral data modeling, database design, database implementation, and data analysis using relational algebra and SQL. Students will generate data models based on real-world problems, and implement a database in a state-of-the-art DBMS. Students will master complex data analysis by learning to first design database queries and then implement them in a database query language such as SQL. Advanced topics include objects in databases, indexing for improved performance, distributed databases, and data warehouses. Prerequisites: Computer Science 225, or consent of instructor. Alternate spring semesters; next offered Spring 2010. (4 credits)

469 DISCRETE APPLIED MATHEMATICS (Same as Computer Science 369)
Topics in applied mathematics chosen from: cryptography; complexity theory and algorithms; integer programming; combinatorial optimization; computational number theory; applications of geometry to tilings, packings, and crystallography; applied algebra. Prerequisites: Mathematics 236 and 379 and Computer Science 121 or 123. Alternate fall semesters; next offered Fall 2008. (4 credits)

471 TOPOLOGY
An introduction to the topology of Euclidean, metric, and abstract spaces. Covers the fundamental ideas from point set topology— continuity, convergence, and connectedness—as well as selected topics from knot theory, three-dimensional manifolds, fixed-point theory, the fundamental group, and elementary homotopy theory. Prerequisite: Mathematics 236 and Mathematics 377. Alternate fall semesters; next offered Fall 2008. (4 credits)

476 TOPICS IN ALGEBRA
Topics in algebra to be chosen from: group representations; algebraic coding theory and finite fields; Galois theory; algebraic and transcendental numbers; ring theory; applied algebra. Prerequisite: Mathematics 376. Alternate fall semesters; next offered Fall 2009. (4 credits)

477 TOPICS IN ANALYSIS
A continuation of Real Analysis including discussion of basic concepts of analysis with particular attention to the development of the Riemann and Lebesgue integrals. Introduction to metric spaces, Fourier analysis. Prerequisite: Mathematics 377. Alternate spring semesters; next offered Spring 2009. (4 credits)

478 COMPLEX ANALYSIS
Algebra of complex numbers, analytic functions, the Cauchy-Riemann equations, Cauchy’s theorem, the Cauchy integral formula, Taylor and Laurent series, the residue theorem, and conformal mapping. Prerequisite: Mathematics 377 or 437. Alternate spring semesters; next offered Spring 2010. (4 credits)

490 SENIOR CAPSTONE SEMINAR
Working with their capstone supervisor, seminar coordinators, and other faculty, students will discuss their capstone project, make presentations of their progress, critique the work of other students, and participate in the activities of the seminar. These activities will include instruction and discussion of strategies for research, writing, and oral presentation. The scheduled times will include both group meetings with other seminar participants as well as individually arranged meetings with the student’s capstone supervisor. Spring semester. S/NC grading only. (1 credit)

604 TUTORIAL
Closely supervised individual (or very small group) study with a faculty member in which a student may explore, by way of readings, short writings, etc., an area of mathematics not available through the regular offerings. Every semester. (1–4 credits)

614 INDEPENDENT PROJECT
Individual project including library research, conferences with instructor, oral and written reports on independent work in mathematics. Subject matter may complement but not duplicate material covered in regular courses. Arrangements must be made with a department member prior to registration. Prerequisite: departmental approval. Every semester. (1–4 credits)

624 INTERNSHIP
Mathematics credit is available to junior and senior students with declared cores or majors in mathematics. Special arrangements must be made well in advance of the regular registration period. Departmental approval and supervision are required. Internships are offered only as S/D/NC grading option. Every semester. (4 credits)

634 PRECEPTORSHIP
Every semester. (4 credits)

644 HONORS INDEPENDENT
Independent research, writing, or other preparation leading to the culmination of the senior honors project. Every semester. (1–4 credits)
Computer Science Course Descriptions
120 INTRODUCTION TO COMPUTING AND ITS APPLICATIONS
Computing and information technology is everywhere, and we live in an increasingly information-oriented society. In this course we define information technology to have five aspects: 1) general-purpose computers and their associated peripheral devices, 2) applications that enable people to make effective use of computing, 3) the data and information stored on these computers, 4) the software that operates the computer and provides us with a human-usable interface, and 5) the theory behind the design of computers and their applications. Because computing permeates virtually every aspect of our lives, it is critically important to have a minimal level of fluency with information technology to enable you to use it effectively in your career as well as your role as a contributing member of society. The aim of this course is to ensure that all students obtain that fluency. No prerequisites. Every semester. (4 credits)

121 INTRODUCTION TO SCIENTIFIC PROGRAMMING
This course is intended to give students from diverse areas of science—e.g., economics, biology, physics, chemistry, geography, geology, mathematics, engineering, statistics—an ability to write software for solving problems and carrying out research in those disciplines. The course provides an introduction to programming and computation as well as to a number of important and widely used techniques: scientific graphics, equation solving, function fitting, optimization, storing and searching data, and simulation. There is an emphasis on ways to represent and transform information on the computer in addition to numbers and text: images, sound, graphs and databases. Prerequisite: No prerequisites. Every fall. (4 credits)

123 CORE CONCEPTS IN COMPUTER SCIENCE
This course introduces the field of computer science, including central concepts such as the design and implementation of algorithms and programs, testing and analyzing programs, the representation of information within the computer, and the role of abstraction and metaphor in computer science. The exploration of these central ideas will draw from the breadth of computer science, with an emphasis on two major application areas: multimedia processing (images, sound, and text) and robotics (control systems for autonomous robots). Course work will use the Python programming language. No prerequisites. Every semester. (4 credits)

124 OBJECT-ORIENTED PROGRAMMING AND DATA STRUCTURES
This course introduces the principles of software design and development using the object-oriented paradigm and the Java programming language. Design techniques covered are programming by contract and Unified Modeling Language (UML) class diagrams. Students will build graphical user interfaces and learn to develop and use abstract data types (ADTs) such as lists, trees, sets, and graphs. Students will study the use of these data structures in applications such as simulation, computational science, and networks. For each ADT, students will analyze their advantages and disadvantages to determine which one works best for a given application. There is a required 1.5 hour laboratory section associated with this course. Prerequisite: Any one of the three introductory courses Computer Science 120, 121, or 123, or consent of instructor. Every semester. (4 credits)

236 LINEAR ALGEBRA
This course blends mathematical computation, theory, abstraction, and application. It starts with systems of linear equations and grows into the study of matrices, vector spaces, linear independence, dimension, matrix decompositions, linear transformations, eigenvectors, and their applications. Prerequisite: Mathematics 136 or Mathematics 137 or, with permission of instructor, Mathematics 135. Every semester. (4 credits)

237 MULTIVARIABLE CALCULUS
Differentiation and integration of functions of two and three variables. Applications of these, including optimization techniques. Also includes introduction to vector calculus, with treatment of vector fields, line and surface integrals, and Green’s Theorem. Prerequisite: Mathematics 137. Every semester. (4 credits)

253 APPLIED MULTIVARIATE STATISTICS
An introduction to multivariate statistical analysis. Emphasizes rationales, applications, and interpretations using advanced statistical software. Examples drawn primarily from economics, education, psychology, sociology, political science, biology and medicine. Topics may include: simple/multiple regression, one-way/two-way ANOVA, logistic regression, discriminant analysis, multivariable correlation. Additional topics may include analysis of covariance, factor analysis, cluster analysis. Prerequisite: Mathematics 154 or 155, or permission of instructor. Every spring. (4 credits)

265 PHILOSOPHY OF MATHEMATICS (Same as Philosophy 365)
Why does 2 + 2 equal four? Can a diagram prove a mathematical truth? Is mathematics a social construction or do mathematical facts exist independently of our knowing them? Philosophy of mathematics considers these sorts of questions in an effort to understand the logical and philosophical foundations of mathematics. Topics include mathematical truth, mathematical reality, and mathematical justifications (knowledge). Typically we focus on the history of mathematics of the past 200 years, highlighting the way philosophical debates arise in mathematics itself and shape its future. Prerequisite: Philosophy 120, Mathematics 136, or permission of the instructor. Alternate years; next offered 2008–2009. (4 credits)

312 DIFFERENTIAL EQUATIONS
After some initial work on first-order equations, much of the course will deal with linear equations and systems using both linear algebra and power series. Applications, some numerical work, and nonlinear techniques. Prerequisite: Mathematics 237. Every fall. (4 credits)

354 PROBABILITY
An introduction to basic probability concepts: sample spaces, probability assignments, combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, functions of random variables, expectation, variance, moment-generating functions, some basic probability processes, and some fundamental limit theorems. Prerequisite: Mathematics 137 (recommended but not required: Mathematics 237). Every fall. (4 credits)

355 MATHEMATICAL STATISTICS
An introduction to the mathematical theory of statistics: sampling distributions, estimation, hypothesis testing, regression. Additional topics may include: analysis of variance and goodness of fit. Emphasis on the theory underlying statistics, not on applications. Prerequisites: Mathematics 354. Every spring. (4 credits)

361 THEORY OF COMPUTATION (Same as Computer Science 261)
A discussion of the basic theoretical foundations of computation as embodied in formal models and descriptions. The course will cover finite state automata, regular expressions, formal languages, Turing machines, computability and unsolvability, and the theory of computational complexity. Introduction to alternate models of computation and recursive function theory. Prerequisite: Computer Science 124, Mathematics 136, or permission of the instructor. Every spring. (4 credits)

365 SCIENTIFIC COMPUTATION (Same as Computer Science 365)
Techniques and algorithms for computational solutions to scientific problems with applications to diverse disciplines. Topics include: numerical integration; root finding; interpolation, splines, and Bezier curves; statistical function estimation; modeling via simulation and Monte Carlo techniques; optimization; transforms; symbolic computing; controlling numerical error. Prerequisites: Computer Science 121 or 123, and Mathematics 137. Linear Algebra (Mathematics 236) not required but strongly recommended. Every spring. (4 credits)

369 ADVANCED SYMBOLIC LOGIC (Same as Philosophy 369)
A second course in symbolic logic which extends the methods of logic. A main purpose of this course is to study logic itself—to prove things about the system of logic learned in the introductory course. This course is thus largely logic about logic. Topics include second order logic and basic set theory; soundness, consistency and completeness of first order logic; incompleteness of arithmetic; Turing computability; modal logic; and intuitionistic logic. Prerequisite: Philosophy 120, Mathematics 135, or permission of instructor. Alternate years; not offered 2008–2009. (4 credits)

371 GEOMETRY
Topics in geometry selected by the instructor. Possible courses include classical Euclidean and non-Euclidean geometry (Hilbert’s axioms; parallel postulate; hyperbolic, elliptic, spherical, projective geometries; Poincare models), differential geometry (calculus on surfaces; curvature; minimal surfaces; geodesics; the Gauss-Bonet theorem), computational geometry (triangulation; point location; Voronoi diagrams; linear programming). Prerequisite: Mathematics 236 and Mathematics 237. Alternate spring semesters; next offered Spring 2010. (4 credits)

373 NUMBER THEORY
An introduction to the properties of and unsolved problems about the integers (whole numbers). This course is built around the problem of proving that a large integer is prime or finding its factorization into primes. Topics include: divisibility and prime numbers, the Euclidean algorithm, modular arithmetic, quadratic residues, continued fractions, and public-key cryptosystems. Prerequisite: Mathematics 136. Alternate fall semesters; next offered Fall 2010. (4 credits)

376 ALGEBRAIC STRUCTURES
Introduction to abstract algebraic theory with emphasis on finite groups, rings, fields, constructibility, introduction to Galois theory. Prerequisite: Mathematics 136 and 236. Every spring. (4 credits)

377 REAL ANALYSIS
Basic theory for the real numbers and the notions of limit, continuity, differentiation, integration, convergence, uniform convergence, and infinite series. Additional topics may include metric and normed linear spaces, point set topology, analytic number theory, Fourier series. Prerequisite: Mathematics 237. Every fall. (4 credits)

379 COMBINATORICS
Advanced counting techniques. Topics in graph theory, combinatorics, graph algorithms, and generating functions. Applications to other areas of mathematics as well as modeling, operations research, computer science and the social sciences. Prerequisites: Mathematics 136, Computer Science 121 or 123 or the equivalent. Alternate fall semesters; next offered Fall 2009. (4 credits)

All 400-level courses will involve some independent student work such as oral presentations, papers, or computer projects.

432 MATHEMATICAL MODELING
Draws on the student’s general background in mathematics to construct models for problems arising from such diverse areas as the physical sciences, life sciences, political science, economics, and computing. Emphasis will be on the design, analysis, accuracy, and appropriateness of a model for a given problem. Case studies will be used extensively. Specific mathematical techniques will vary with the instructor and student interest. Prerequisites: Mathematics 312, and Computer Science 121 or 123. Alternate fall semesters; next offered Fall 2009. (4 credits)

437 CONTINUOUS APPLIED MATHEMATICS
Transforms and their applications. Topics selected from among: the Fourier transform and applications in partial differential equations and signal and image processing; the Laplace transform in control theory; wavelet analysis. Prerequisites: Mathematics 236 and 312. Alternate spring semesters; next offered Spring 2009. (4 credits)

MATH 108 QUANTITATIVE THINKING FOR POLICY ANALYSIS (same as Economics 108)
Students will learn related approaches to collecting, interpreting, and presenting quantitative information in the context of specific public policy issues such as immigration, globalization, discrimination, health care, and environmental issues. The course will build on familiar numerical, statistical, and logical skills. No prerequisites. Every semester. (4 credits)

116 MATHEMATICS—ITS CONTENT AND SPIRIT
Introduction to a spectrum of modern applications of mathematics. Case studies will be taken from a range of fields, including mathematics, economics, political science, environmental science, computer science, and the fine arts. Focus is on understanding where and how mathematics can be used in a social, political, or civic setting. The course is designed for students looking to fulfill the natural sciences and mathematics distribution requirement. Example topics might include game theory, voting systems, symmetry and patterns, risk analysis, coding theory and cryptography. No prerequisites. Alternate spring semesters; next offered Spring 2010. (4 credits)

135 APPLIED CALCULUS
This introductory-level course focuses on those aspects of calculus that are particularly useful in applied work in the natural and social sciences. There is a strong emphasis on developing mathematical modeling skills. The topics include differential calculus of functions of one and several variables, differential and difference equations, and the geometry of high-dimensional space. Case studies are drawn from varied areas, including biology, economics, and physics. The course is designed both for students with no previous calculus, and students who have had one or two semesters of AP calculus (but who do not intend directly to take Mathematics 236 or 237). Every semester. (4 credits)

136 DISCRETE MATHEMATICS
An introduction to the basic techniques and methods used in combinatorial problem-solving. Includes basic counting principles, induction, logic, recurrence relations, and graph theory. Every semester. (4 credits)

137 SINGLE VARIABLE CALCULUS
Differentiation and integration of functions of a single variable, with applications. Main topics: Limit definition of the derivative and integral, exponential growth, chain rule, Riemann sums, numerical integration, integration by substitution and parts, improper integrals, geometric series, Taylor polynomials. This is a more in-depth course than Mathematics 135, and should be taken instead of Mathematics 135 by students intending to continue in mathematics. Prerequisites: High school calculus or Mathematics 135. Every semester. (4 credits)

153 DATA ANALYSIS AND STATISTICS
An introduction to basic concepts of data analysis and statistics in the spirit of the liberal arts. Emphasis on data analysis, model assumptions, and interpreting results. Examples and techniques drawn primarily from the social sciences. Major topics: uncertainty/variation, data acquisition, graphical techniques, descriptive statistics, exploratory versus confirmatory analysis, statistical inference. Recommended for students in humanities/fine arts/social sciences and/or those not planning to pursue careers in quantitative analysis; prospective economics majors are encouraged to take Mathematics 155. Students who successfully complete this course cannot receive credit for Mathematics 154. Prerequisite: High school algebra. Every semester. (4 credits)

155 INTRODUCTION TO STATISTICAL MODELING
An introductory statistics course with an emphasis on multivariate modeling. Topics include descriptive statistics, experiment and study design, probability, hypothesis testing, multivariate regression, single and multi-way analysis of variance, logistic regression. Prerequisites: Mathematics 135 or Mathematics 236 or Mathematics 237 or permission of instructor. Every semester. (4 credits)

The Mathematics and Computer Science department is the largest department at Macalester. It offers majors and minors in Mathematics and in Computer Science, and a minor in Statistics. There are 12 full-time faculty members in the department and approximately 30-40 graduating majors each year.

We have close ties with economics, biology, chemistry, and physics departments, the neuroscience program, and other social science departments through our work on quantitative reasoning.

Mathematics Our mathematics major has two paths that students choose between – one in mathematics and one in applied mathematics and statistics. This produces a flexible major that can be tailored to individual interests and ambitions.

Computer Science Our computer science major and minor cover the theoretical foundations of computation such as automata, algorithms, and languages as well as important areas of application: modern software development, networks, operating systems, parallel programming, databases, and artificial intelligence. Our introductory course sequence prepares students to follow either a theoretical or application-driven path.

Statistics Our statistics minor offers students the ability to develop important skills in the analysis of data from varied sources and to master the modern conceptual apparatus that influenced all areas of the natural and social sciences.