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Department of Mathematical Sciences

Bachelor of Science

Bachelor of Arts

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The Mathematical Sciences curriculum, carefully designed to possess a high degree of versatility, equips the student with the knowledge of mathematical concepts and methods that are applicable in physics, computer science, communication theory, data processing, statistics, operations research, economics, or any branch of the physical sciences in which a strong mathematical background is desired. In addition to containing the basic courses which provide the student with the skills necessary in the use of mathematics as it relates to other fields, the curriculum allows the student in his or her junior year to select one of five optional sets of courses, providing an introduction to an area where mathematics is applied. These options are Applied Analysis, Biology, Computer Science, Operations Research/Management Sciences, Statistics. In addition to the overall goal of preparing the student to cope with the dynamics of any mathematical environment, the curriculum seeks to provide an adequate background for the student who plans to pursue graduate study in mathematics or to fill many interesting positions in space research, computer development, business, or government research. Those electing the Biology option will have the necessary preparation for entering medical school.

Freshman Year

First Semester

Total: 17

Second Semester

Total: 17

Sophmore Year

First Semester

Total: 15

Second Semester

Total: 17

Junior Year

First Semester

Total: 16

Second Semester

Total: 16

Senior Year

First Semester

Total: 16

Second Semester

Total: 16

130 Total Semester Hours

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OPTIONS

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Operations Research/Management Science(See note on Economics Requirement)

Total: 15

Statistics

Total: 12

Applied Analysis

Total: 12

Foreign Languages Requirement

Eight semester hours in the same language are required.

Approved Courses

These requirements must he approved by the advisor.

Literature Requirement

ENGL 202, 203, 204, 205, 206, 207, 208, 209.

Science Requirement

Must include two of the following sequences:BIOL 103, 104; CH101,102, or 112; ECON 314,405; PHYS 221/223,222/224.

Application Area

These courses must be approved by the advisor. Possibilities include CH 331 332; E M 320; MTHSC 457, 458; PHYS 321, 322, 441, 442; M E 302.

Economics Requirements

ECON 314, 405.

Notes:

BIOLOGY

Freshman Year

First Semester

Total: 15

Second Semester

Total: 16

Sophmore Year

First Semester

Total: 18

Second Semester

Total: 18

Junior Year

First Semester

Total: 16

Second Semester

Total: 16

Senior Year

First Semester

Total: 16

Second Semester

Total: 15

130 Total Semester Hours

Advanced Placement Credits - Biology Option

Those qualifying for advanced placement in languages or wanting to take languages the freshman year may take them in place of these courses.

Literature Requirement - Biology Option

ENGL 202, 203, 204, 205, 206, 207, 208, 209.

Foreign Language - Biology Option

In the same language.

Animal or Plant Diversity Requirement

BlOSC 302, 303, 304, 305.

Biological Science Requirement

Select from BIOCH 301, GEN 302, MICRO 305 or any 300- and 400-level biological science or zoology course.

Notes:

Computer Science Option

Freshman Year

First Semester

Total: 17

Second Semester

Total: 17

Sophmore Year

First Semester

Total: 16

Second Semester

Total: 17

Junior Year

First Semester

Total: 15-16

Second Semester

Total: 16

Senior Year

First Semester

Total: 16-18

Second Semester

Total: 16

130 Total Semester Hours

Foreign Language Requirement

Eight semester hours in the same language are required.

Literature Requirement

ENGL 202, 203, 204, 205, 206, 207, 208, 209.

Social Sciences Requirement

Must be approved by advisor.

Mathematical Sciences Requirement

Select from 300- and 400-level MTHSC courses with approval of advisor.

Sciences Requirement

Must include two of the following sequences: BIOL 103, 104; CH 101,102 or 112;ECON 314,405;PHYS 221/223,222/224.

Computer Sciences Requirement

Choose one of the following sequences: CP SC 231, 428; 350, 450; 360, 462 or any two courses from CP SC 231, 350, 360, 372 or MTHSC 461.

Notes:

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Department of Mathematical Sciences

Bachelor of Arts

Bachelor of Sciences

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Freshman Year

First Semester

Total: 17

Second Semester

Total: 17

Sophmore Year

First Semester

Total: 15

Second Semester

Total: 17

Junior Year

First Semester

Total: 17

Second Semester

Total: 17

Senior Year

First Semester

Total: 15

Second Semester

Total: 15

130 Total Semester Hours

Foreign Language Requirement

Four semesters of the same language.

Literature Requirement

ENGL 202, 203, 204, 205, 206, 207, 208, 209.

Social Sciences Requirement

Must be approved by advisor.

Mathematical Sciences Requirement

Select from 300- and 400-level MTHSC courses with approval of advisor. ===========================================================

Department of Mathematical Sciences

Course Listings

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MTHSC 101 Finite Probability 3(3,0)

Topics in include probability, discrete random variables, and probability distributions. May not be taken by students who have successfully completed MTHSC 301. Preq: A satisfactory score on the Mathematics Test, Level II (Standard) or consent of instructor .

MTHSC 102 Introduction to Mathematical Analysis 3(3,0)

An intuitive approach to the concepts and applications of calculus. Topics include functions and graphing, differentiation, and integration. Applications from social, biological, and management sciences are presented. Not open to those receiving credit for MTHSC 106. Preq: A satisfactory score on the Mathematics Test, Level II (Standard) or consent of instructor

MTHSC 104 College Algebra 3(3,1)

Basic course in college algebra designed to prepare students for more advanced courses in finite probability, mathematical analysis, and elementary statistics. Fundamental concepts of algebra, algebraic equations and inequalities, functions and graphs will be studied. Students who have received credit for MTHSC 102 or 105 or 106 will not be allowed to enroll in or receive credit for MTHSC 104.

MTHSC 105 Precalculus 5(5,1)

Extensive treatment of topics chosen to prepare students for the study of calculus. Special emphasis is given to polynomial, rational, exponential, logarithmic and trigonometric functions and their graphs, as well as basic and analytic trigonometry. Students who have received credit for MTHSC 102 or 104 or 106 will not be allowed to enroll in or receive credit for MTHSC 105.

MTHSC 106, H106 Calculus of One Variable 1 4(4,0)

Topics include analytic geometry, introduction to derivatives, computation and application of derivatives, integrals, exponential and logarithm functions. Preq: MTHSC 105, or a satisfactory score on the Mathematics Test, Level II (Standard) or consent of instructor.

MTHSC 108, H108 Calculus of One Variable II 4(4,0)

Topics include infinite series limits, differentiation and techniques of integration. Preq: MTHSC 106.

MTHSC 109 Algebra and Trigonometry for Teachers 3(3,0)

Unified course in algebra and trigonometry. Complex number system, functions, graphs, solving equations and inequalities, trigonometry, sequences, series, combinations, and permutations. A refresher course for teachers assigned to teach in a school's college preparatory program. Enrollment limited to in-service teachers.

MTHSC 110 Analytic Geometry for Teachers 3(3,0)

Algebraic techniques applied to geometry; lines, conic sections and their graphs; transformations of coordinates; general second-degree equations: parametric equations; polar coordinates. Restricted to in-service teachers. Preq: MTHSC 109 or equivalent.

MTHSC 115 Contemporary Mathematics for Elementary School Teachers I 3(3,0)

Logic, sets, and the properties of the counting numbers, numeration systems. Open to Elementary Education majors only. Preq: A satisfactory score on the Mathematics Test Level II.

MTHSC 116 Contemporary Mathematics for Elementary School Teachers 113(3,0)

Continuation of MTHSC 115. Subtraction, properties of the integers, elementary number theory, rational number system, real number system. Open to Elementary Education majors only. Preq: MTHSC 115 or consent of instructor.

MTHSC 119 Introduction to Discrete Methods 3(3,0)

Topics normally will include elementary logic and methods of proof: sets, functions, and relations; graphs and trees; combinatoral circuits and Boolean Algebra. Preq: Satisfactory score on the Mathematics Test, Level II (Standard).

MTHSC 129 Problem Solving in Discrete Mathematics 3(2,2)

A problem-solving approach to learning mathematics will be applied to topics in modern discrete mathematics. Typical selection of topics will include logic and proof, sets, relations, functions, mathematical induction, graphs and trees, counting techniques, recurrence equations. For Bachelor of Science and Bachelor of Arts majors in Mathematical Sciences only. Credit may not be received for both MTHSC 119 and MTHSC 129. Preq: MTHSC 106.

MTHSC 203 Elementary Statistical Inference 3(3,0)

Survey course in fundamental statistical principles with applications. Topics include estimation, tests of hypotheses, regression and correlation, analysis of variance, and nonparametric statistics May not be taken by students who have passed MTHSC 301. Preq: MTHSC 101.

MTHSC 206, H206 Calculus of Several Variables 1(4,0)

Topics include real valued functions of several variables, multiple integration, differential calculus of functions of several variables, vector field theory. Preq: MTHSC 108.

MTHSC 207 Multivariable Calculus 3(3,0)

Introduction to the calculus of several variables, differential calculus and optimization of several variables, multiple integrals. Topics from the management sciences will be used to illustrate the above concepts. May not be taken by students who have passed MTHSC 206. Preq: MTHSC 102, or 106 with consent of instructor.

MTHSC 208, H208 Introduction to Ordinary Differential Equations 4(4,0)

Introduction to the study of differential equations and their application to physical problems. Topics include exact, series and numerical solutions; solutions by means of Laplace transforms; and solutions of systems of differential equations. Preq: MTHSC 206.

MTHSC 210 Applied Matrix Algebra 3(3,0)

Introduction to the basic principles of matrix algebra with applications to the behavioral and managerial sciences. The major areas of application will include linear programming, directed graphs, and game theory. Preq: MTHSC 101 and MTHSC 102 or 106.

MTHSC 216 Geometry for Elementary School Teachers 3(3,0)

An informal treatment of the basic concepts of geometry. Open to Elementary Education majors only. Preq: MTHSC 116 or consent of instructor.

MTHSC 231 Mathematics of Life Insurance 3(3,0)

Introduction to the basic mathematics of finance and life insurance. Topics include compound interest, annuities certain, mortality tables, life annuities, net premiums, net level reserves, modified reserves, nonforteiture values and dividends.

MTHSC 232 Actuarial Science Seminar I 1(1,0)

Problem-solving seminar designed to prepare the student for the Society of Actuaries Examination I (General Mathematics). Preq: MTHSC 206.

MTHSC 250 Introduction to Mathematical Sciences 1(1,0)

Lectures and discussions on the mathematical sciences disciplines: Applied Mathematics, Computing Science. Core Mathematics, Management Science, Operations Research, and Statistics. Preq: MTHSC 106.

MTHSC 301, H301 Statistical Theory and Methods I 3(3.0)

Principal topics include elementary probability theory, discrete and continuous random variables, expected values, normal distribution, chi-square distribution, t-distribution, F-distribution, tests of hypotheses, point and interval estimation, curve fitting. Preq: MTHSC 106 or 207 or 210.

MTHSC 302 Statistics for Science and Engineering 3(3,0)

Methodology for collecting, organizing and interpreting data. Topics include understanding variability, graphical and numerical summarization of data, introductory probability, normal and related distributions statistical inference, experimental design, simple linear regression. Statistical microcomputer software will be used. Preq: MTHSC 106.

MTHSC 308 College Geometry 3(3,0)

Theorems and concepts more advanced than those of high school geometry. A treatment of the various properties of the triangle, including the notable points, lines, and circles associated with it. Preq: MTHSC 106.

MTHSC 311, H311 Linear Algebra 3(3,0)

Introduction to the algebra of matrices, vector spaces, polynomials, and linear transformations. Preq: MTHSC 108 or consent of instructor.

MTHSC 360 Intermediate Mathematical Computing 3(3,0)

Continuing study of mathematical computing using the FORTRAN language. Emphasis on subroutine computation with applications to problems in science and engineering. Preq: CP SC 110 or consent of instructor.

MTHSC 400, H400, 600 Theory of Probability 3(3,0)

Principal topics include combinatorial theory, probability axioms, random variables, expected values special discrete and continuous distributions, jointly distributed random variables, correlation, conditional expectation, law of large numbers, central limit theorem. Preq: MTHSC 206 or consent of instructor.

MTHSC 401, H401, 601 Statistical Methodology 3(3,0)

Probability-based treatment of statistical methods. Topics include point and interval estimation, hypothesis testing, analysis of variance, regression and correlation, analysis of categorical data, and distribution-free& procedures. Preq: MTHSC 311 and 400.

MTHSC 403, H403, 603 Introduction to Statistical Theory 3(3,0)

Principal topics include sampling distributions, point and interval estimation, maximum likelihood estimators, method of moments, least squares estimators, tests of hypotheses, likelihood ratio methods, regression and correlation analysis, introduction to analysis of variance. Preq: MTHSC 400 or equivalent.

MTHSC 405, 605 Statistical Theory and Methods II 3(3,0)

Principal topics include simple linear regression, multiple regression and correlation analysis one-way analysis of variance multiple comparison, multifactor analysis of variance, experimental design. Computation and interpretation of results are facilitated through use of statistical computer packages. Preq: MTHSC 301.

MTHSC 406, 606 Sampling Theory and Methods 3(3,0)

Probability-based treatment of sampling methodology. Theory and application of estimation techniques will be treated using simple and stratified random sampling, cluster sampling, and systematic sampling. Coreq: MTHSC 401.

MTHSC 407, 607 Regression and Time-Series Analysis 3(3,0)

Theory and application of the regression and time series approaches to empirical model building and data analysis are treated. Computation and interpretation of results are facilitated through the use of interactive statistical packages. Preq: MTHSC 401.

MTHSC 408, 608 Topics in Geometry 3(3,0)

Introduction to topics in special geometries which include non-Euclidean: space concepts such as projective geometry, finite geometries, and intuitive elementary topology. A brief introduction to vector geometry. Preq: MTHSC 206.

MTHSC 410 Number Theory 3(3,0)

Introduction to the theory of integers and related number systems. Topics include historical development, principle of mathematical induction, divisibility primes Congruences, number-theoretic functions, primitive roots, quadratic residues, and diophantine equations. Preq: MTHSC 108 or consent of instructor.

MTHSC 412, H412, 612 Introduction to Modern Algebra 3(3,0)

Introduction to the concepts of algebra. Topics included are the number system and the elementary theory of groups, rings, and fields. Preq.: MTHSC 311.

MTHSC 419, H419, 619 Discrete Mathematical Structures 1 3(3,0)

This course applies theoretical concepts of sets, functions, binary relations, graphs, Boolean algebras, propositional logic, semigroups, groups, homomorphisms, and permutation groups to computer characteristics and design, words over a finite alphabet and concatenation, binary group codes, and other communication or computer problems. Preq: MTHSC 311.

MTHSC 425, H425 Orthogonal Functions and Boundary Value Problems 3(3,0)

Continuation of MTHSC 208. Introduction to Fourier Series, numerical methods, partial differential equations, and certain special functions is given. Preq: MTHSC 208.

MTHSC 432 Actuarial Science Seminar II 1(1,0)

Problem-solving seminar designed to prepare the student for the Society of Actuaries Examinations 2 (probability and statistics). Preq: MTHSC 403 may be taken concurrently or consent of instructor.

MTHSC 434,634 Advanced Engineering Mathematics 3(3,0)

Fourier series, Laplace and Fourier transform and numerical methods for solving initial value and boundary-value problems in partial differential equations are developed. Applications to diffusion wave and Dirichlet problems are given. Matrix methods and special functions are utilized. Preq: MTHSC 208.

MTHSC 435, H435, 635 Complex Variables 3(3,0)

Elementary functions. Differentiation and integration of analytic functions, Taylor and Laurent series. Contour integration and residue theory, conformal mapping, Schwartz-Christoffel transformation. Preq: MTHSC 206.

MTHSC 440, H440, 640 Linear Programming 3(3,0)

Introduction to linear programming covering the simplex algorithm, duality, sensitivity analysis, network models, formulation of models, and the use of simplex codes to solve, interpret, and analyze problems. Preq: MTHSC 206, 311, or consent of instructor.

MTHSC 441, H441, 641 Introduction to Stochastic Models 3(3,0)

Introductory treatment of stochastic processes, finite-state Markov chains, queueing, dynamic programming Markov decision processes, reliability, decision analysis and simulation. Both theory and applications will be stressed. Preq: MTHSC 400.

MTHSC 450 Introduction to Mathematical Models 3(3,0)

Study of the modeling process which will include the translation of practical problems into mathematical models, the solution of the mathematical models, and the interpretation of the solution back into practical problems. Examples will be chosen from the physical, biological, social, and management sciences. Preq: CP SC 110, MTHSC 208. Coreq: MTHSC 401 or consent of instructor.

MTHSC 453, H453, 653 Advanced Calculus I 3(3,0)

Limits, continuity, and differentiation of functions of one and several variables, the Riemann integral, and vector analysis. Preq: MTHSC 206.

MTHSC 454 H454, 654 Advanced Calculus II 3(3,0)

Continuation of MTHSC 453. Transformations, multiple integrals line and surface integrals, infinite sequences and series, and improper integrals.

MTHSC 460, 660 Introduction to Numerical Analysis I 3(3,0)

Introduction to the problems of numerical analysis emphasizing computational procedures and application. Topics include sources of error and conditioning, matrix methods, systems of linear equations, nonlinear equations, interpolation and approximation by splines, polynomials and trigonometric functions. Preq: MTHSC 206 or MTHSC 207 and MTHSC 360 or equivalent.

MTHSC 463, H463, 663 Mathematical Analysis 1 3(3,0)

Basic properties of the real number system, sequences and limits; continuous functions, uniform continuity and convergence. Integration, differentiation, functions of several real variables, implicit function theory. Preq: MTHSC 206.

MTHSC 464, H464, 664 Mathematical Analysis II 3(3,0)

Continuation of MTHSC 463 .

MTHSC 481 Seminar in Mathematics 1-3(1-3,0)

Attention will be focused upon mathematical areas in which nonroutine problems can be posed with comparative ease. Emphasis will be upon independent study and student use of previously acquired mathematical skills. Open to students only by invitation for not more than 3 hours credit.

Credit toward graduation will be given for only one of the following: EX ST 301. MTHSC 301, 302.

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This is a project of the Ad Hoc Committee on Recruitment, Advising and Retention of the Department of Mathematical Sciences

Author: Calvin L. Williams, Mathematical Sciences-Clemson University, Clemson University
Last updated: March 30, 1997
Send Comments to : calvinw@math.clemson.edu