# MATHEMATICAL SCIENCES

**MTHSC 101 Essential Mathematics for the Informed
Society 3(3,0)** Topics include logic and computers, probability and
statistics, and financial mathematics. Specific topics include Boolean algebra,
digital data formats, randomness, graphical representation of data, inference
and estimation; interest, annuities, and amortization. Not open to students who
have received credit for MTHSC 301, 302, 309, or EX ST 301. Preq: Satisfactory
score on the Clemson Mathematics Placement Test or consent of department.

**MTHSC 102 Introduction to Mathematical Analysis 3(3,0)**
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 students
who have received credit for MTHSC 106. Preq: Satisfactory score on the Clemson
Mathematics Placement Test or consent of department.

**MTHSC 103 Elementary Functions 3(2,2)** Gateway
course for MTHSC 106. Comprehensive treatment of functions and analytic geometry
with applications including polynomial, rational, algebraic, exponential,
logarithmic, and trigonometric functions. Not open to students who have received
credit for MTHSC 105. To be taken Pass/Fail only. Preq: MTHSC 104 or
satisfactory score on the Clemson Mathematics Placement Test.

**MTHSC 104 College Algebra 3(2,2)** Basic course to
prepare students for subsequent courses in probability, mathematical analysis,
elementary statistics, and elementary functions (precalculus). Fundamental
concepts of algebra, equations, inequalities, functions, and graphs are studied.
Students who have received credit for any other mathematical sciences course
will not be allowed to enroll in or receive credit for MTHSC 104. To be taken
Pass/Fail only.

** MTHSC 105 Precalculus 5(4,2)** 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 any other mathematical sciences course will not be
allowed to enroll in or receive credit for MTHSC 105. To be taken Pass/Fail
only.

**MTHSC 106, H106 Calculus of One Variable I 4(4,0)**
Topics include analytic geometry, introduction to derivatives, computation and
application of derivatives, integrals, exponential and logarithm functions. Preq:
MTHSC 103 or 105 or satisfactory score on the Clemson Mathematics Placement Test
or consent of department.

**MTHSC 107 Co-Calculus I 1(0,2) **Recitation course to
accompany MTHSC 106. Reinforces precalculus and calculus topics covered in MTHSC
106 and provides additional instruction and practice for students. Required of
students identified by the Clemson Mathematics Placement Test as being
conditionally qualified for placement in calculus with supplemental instruction.
To be taken Pass/Fail only. Preq: Concurrent enrollment in MTHSC 106.

**MTHSC 108, H108 Calculus of One Variable II 4(4,0**)
Topics include transcendental functions, applications of integration,
integration techniques, indeterminate forms, improper integrals, parametric
equations, polar coordinates, and infinite series. Preq: MTHSC 106.

**MTHSC 109 Co-Calculus II 1(0,2)** Recitation style
course to accompany MTHSC 108. Reinforces precalculus and calculus topics
covered in MTHSC 108 and provides additional instruction and practice.
Recommendations are made to students based on their scores on a Calculus Basic
Skills Quiz, given at the beginning of each semester. Preq: Concurrent
enrollment in MTHSC 108.

**MTHSC 115 Contemporary Mathematics for Elementary
School Teachers I 3(3,0)** Cooperative learning groups, manipulatives, and
concrete models are used to demonstrate logical reasoning, problem-solving
strategies, sets and their operations, numeration systems, properties and
operations of whole numbers, number theory, prime and composite numbers,
divisibility, common factors and multiples. Open to Elementary, Early Childhood,
and Special Education majors only. Preq: MTHSC 104 or satisfactory score on the
Clemson Mathematics Placement Test.

**MTHSC 116 Contemporary Mathematics for Elementary
School Teachers II 3(3,0)** Continuation of MTHSC 115. Manipulatives and
concrete models are used for properties, operations, and problem solving for
integers, elementary fractions, rational numbers, and real numbers. Selected
topics in statistics and probability are introduced with a hands-on approach to
learning. Restricted to Elementary, Early Childhood, and Special Education
majors. Preq: MTHSC 115 or consent of instructor.

**MTHSC 117 Mathematics for Elementary School Teachers I
3(2,2)** Problem-solving strategies, logic, algebraic thinking, sets,
relations, functions, numeration systems, whole numbers, integers, number
theory, fractions, decimals, applications of percent, real numbers with their
computational algorithms and properties are explored. Content, according to
state standards, is taught with appropriate methodology for teaching K-6. Preq:
MTHSC 101.

**MTHSC 118 Mathematics for Elementary School Teachers II
3(2,2)** Simple probability and descriptive statistics are reviewed. Two- and
three-dimensional geometry including polygons, polyhedra and their properties;
congruence, similarity, and constructions; coordinate system; standard
measurement, area, surface area, volume; and motion geometry are explored.
Content, according to State standards, is taught with appropriate methodology
for teaching K-6. Preq: MTHSC 117.

**MTHSC 119 Introduction to Discrete Methods 3(3,0)**
Topics normally include elementary logic and methods of proof; sets, functions,
and relations; graphs and trees; combinatorial circuits and Boolean Albegra.
Preq: Satisfactory score on the Clemson Mathematics Placement Test or consent of
department.

**MTHSC 129 Problem Solving in Discrete Mathematics
3(2,2)** Problem-solving approach to learning mathematics is applied to topics
in modern discrete mathematics. Typical selection of topics includes 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 129. Preq: MTHSC 106.

**MTHSC 199 Problem Solving in Mathematics 3(2,2)**
Functions and graphs, mathematical modeling, and applications. Applications from
management and life and social sciences are presented. Specific topics include
linear, quadratic, polynomial, exponential, and logarithmic functions with
emphasis on problem solving. Students who have received credit for any other
mathematical sciences course will not be allowed to enroll in or receive credit
for MTHSC 199. To be taken Pass/Fail only.

**MTHSC 203 Elementary Statistical Inference 3(3,0)**
Data-based course in statistical methodology: collecting and summarizing data,
the normal distribution, one and two sample inference on means and proportions,
simple linear regression, analysis of categorical data. May not be taken for
credit by students who have passed MTHSC 301, 302, 309, or EX ST 301. Preq:
Satisfactory score on the Clemson Mathematics Placement Test or MTHSC 101 or
consent of department.

**MTHSC 206, H206 Calculus of Several Variables 4(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 are 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. Major areas of application include linear
programming, directed graphs, and game theory. Preq: MTHSC 101 and 102 or 106.

**MTHSC 216 Geometry for Elementary School Teachers
3(3,0) **Informal treatment of the basic concepts of geometry. Open to
Elementary, Early Childhood, and Special Education majors only. Preq: MTHSC 116
or consent of instructor.

**MTHSC 231 Mathematics of Life Insurance 3(3,0)**
Introduction to basic mathematics of finance and life insurance. Topics include
compound interest, annuities certain, mortality tables, life annuities, net
premiums, net level reserves, modified reserves, nonforfeiture values, and
dividends.

**MTHSC 250 Introduction to Mathematical Sciences 1(1,0)**
Introduction to areas of study, degree options, career choices, and professional
development in mathematical sciences. Includes guidelines and requirements for
portfolio development and an introduction to ethical issues.

**MTHSC 299 Creative Inquiry-Mathematical Sciences
1-3(1-3,0)** In consultation with and under the direction of a faculty member,
students pursue scholarly activities individually or in teams. These creative
inquiry projects may be interdisciplinary. Arrangements with mentors must be
established prior to registration. May be repeated for a maximum of three
credits.

**MTHSC 301, H301 Statistical Methods I 3(3,0)**
Principal topics include collecting and summarizing data, probability
distributions, inferences about central values and variation, analysis of
categorical data, simple linear regression, basic experimental designs, and the
analysis of variance. Credit toward a degree will be given for only one of MTHSC
301, 302, 309, EX ST 301. 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 is used. Credit toward a degree will be given for only
one of EX ST 301, MTHSC 301, 302, 309. Preq: MTHSC 206.

**MTHSC 308 College Geometry 3(3,0)** Theorems and
concepts more advanced than those of high school geometry. Treatment of the
various properties of the triangle, including the notable points, lines, and
circles associated with it. Preq: MTHSC 106.

**MTHSC 309 Introductory Business Statistics 3(3,0)**
Introductory probability and statistics for business students, particularly
those who will take MGT 310. Topics include descriptive statistics, probability,
expectations, binomial, normal, sampling distributions, one and two sample
estimation and testing. Credit toward a degree will be given for only one of EX
ST 301, MTHSC 301, 302, 309. Preq: MTHSC 106 or 207 or 210.

**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)**
Intermediate-level introduction in using computers to solve problems in the
mathematical sciences. Fundamental concepts of procedural programming including
flow control, modular construction, primitive data structures, recursion, and
graphics are applied to problems in applied mathematics, probability,
statistics, discrete mathematics, and operations research.Preq: MTHSC 108.

**MTHSC H382 Honors Seminar 1(1,0)** Weekly seminar to
prepare students in Departmental Honors Program for independent senior research.
At the end of the second semester, each student must have identified a research
topic and a faculty advisor. May be repeated for a maximum of two credits. Preq:
Junior standing in departmental honors program.

**MTHSC 399 Creative Inquiry-Mathematical Sciences
1-3(1-3,0)** In consultation with and under the direction of a faculty member,
students pursue scholarly activities individually or in teams. These creative
inquiry projects may be interdisciplinary. Arrangements with mentors must be
established prior to registration. May be repeated for a maximum of three
credits.

**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 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 are treated using simple and stratified random sampling,
cluster sampling, and systematic sampling. Preq: MTHSC 302 and 400, or consent
of instructor.

**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 302, 311, 400; or consent of instructor.

**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. Brief introduction to vector geometry. Preq: MTHSC 206.

**MTHSC 410 Number Theory 3(3,0) **Introduction to
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 include the number
system and the elementary theory of groups, rings, and fields. Preq: MTHSC 311.

**MTHSC 419, H419, 619 Discrete Mathematical Structures I
3(3,0**) 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 430 Actuarial Science Seminar I 1(1,0)**
Problem-solving seminar to prepare students for the Society of Actuaries' Exam P
or the Casualty Actuarial Society's Exam I (Probability). Preq: MTHSC 400 or
consent of instructor.

**MTHSC 431 Theory of Interest 3(3,0)** Comprehensive
treatment of the theory of interest including from a calculus-based continuous
viewpoint. Topics include simple and compound interest and discount, nominal and
effective rates, force of interest, basic and general annuities, yield rates,
amortization and sinking funds, and applications to bonds, mortgages, and other
securities. Preq: MTHSC 206.

**MTHSC 432 Actuarial Science Seminar II 1(1,0)**
Problem-solving seminar to prepare students for the examination on the Society
of Actuaries' and Casualty Actuarial Society's Course 2 (Interest Theory,
Economics and Finance). Preq: ECON 211, 212, FIN 306 or 311, MTHSC 431, 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 Dirichelet 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 are stressed.
Preq: MTHSC 400.

**MTHSC 450 Introduction to Mathematical Models 3(3,0)**
Includes a study of the modeling process and examples of existing models chosen
from physical, biological, social, and management sciences, depending on the
instructor. Written and oral report is required for at least one of the models
studied. May be repeated for a maximum of six credits. Preq: MTHSC 302, 360,
440, 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. Preq: MTHSC
453.

**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, polynominals, and trigonometric
functions. Preq: MTHSC 206 or 207 and 360 or equivalent.

**MTHSC 463, H463, 663 Mathematical Analysis I 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 481 Seminar in Mathematics 1-3(1-3,0)**
Attention is focused on mathematical areas in which nonroutine problems can be
posed with comparative ease. Emphasis is on independent study and student use of
previously acquired mathematical skills. Open to students by invitation only for
a maximum of three credits.

**MTHSC 482, H482 Undergraduate Research 3(3,0) **
Independent research conducted under the supervision and guidance of a faculty
member. May be repeated for a maximum of six credits.

**MTHSC 491 Independent Study 3(3,0)** Independent
study or internship in mathematical sciences under faculty supervision. A
written report and oral poster presentation of the results of the independent
study or internship are required. May be repeated for a maximum of six credits.
Preq: Mathematical Sciences major.

**MTHSC 492 Professional Development 1(1,0)** Issues in
professional development in the Mathematical Sciences. Individual portfolios are
evaluated and critiqued for continued career use. To be taken Pass/Fail only.

**MTHSC 499 Creative Inquiry-Mathematical Sciences
1-3(1-3,0) **In consultation with and under the direction of a faculty member,
students pursue scholarly activities individually or in teams. These creative
inquiry projects may be interdisciplinary. Arrangements with mentors must be
established prior to registration. May be repeated for a maximum of three
credits.

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