ISU 2011-12 Undergraduate Catalog

Idaho State University Undergraduate Catalog 2011-2012

Department of Mathematics

Chair and Professor: Fisher
Assistant Chair and Professor: Laquer
Professors: Egger, Gryazin, Hanin, R. Hill, Kriloff, Lang, Palmer, Payne, Stowe, Wolper
Associate Professors: Chen, Gironella
Assistant Professors:  Derryberry, Zhu
Senior Lecturers: Walker, Yost
Associate Lecturers: England, Kress, Martin, Miller, Mills, Potter
Assistant Lecturers: Jones, Reed
Visiting Assistant Lecturer: Zhong
Part-time Adjunct Faculty: Barclay, Christensen, Dewey, Harmon, Horwith, Judy, Lundeen, Mayes, Rude
Emeriti: Cresswell, Ford, L. Hill, Kratz, Parker


 Faculty Information   
 Department Web Page   
 Program Objectives    
Associate of Science in Mathematics   
Bachelor of Science in Mathematics   
Bachelor of Science in Statistics   
Minor in Applied Mathematics   
Minor in Mathematics   
Minor in Statistics   
Mathematics Courses   

The undergraduate programs in Mathematics have the following objectives:

  1. Students in algebra courses develop the algebra skills needed in later courses.
  2. Students in general education courses gain an understanding of mathematics as a language in which to express, define, and answer questions about the world.
  3. Students in courses that serve the sciences and engineering, particularly calculus and linear algebra courses, develop technical skills, learn to apply mathematical tools, and develop an understanding of the mathematical basis for those tools.
  4. Students in statistics courses develop an understanding of the basic concepts of probability and statistics and learn how to use statistical tools in real-life problems.
  5. Education students with a mathematics teaching major or minor gain a basic understanding of several areas of mathematics, develop a sense for exploring mathematics, and learn to read, write, and present mathematics.
  6. Mathematics majors become acquainted with the major branches of the discipline; learn to read and write mathematics; and develop the mathematical skills and general knowledge necessary for employment or for graduate work in mathematics or other fields.


Mathematics Core

All Bachelor's degrees offered by the Department of Mathematics have a common core consisting of the following six courses (21 credits):
CS 1181 	Computer Science and Programming I 	3 cr
MATH 1170 	Calculus I 				4 cr
MATH 1175 	Calculus II 				4 cr
MATH 2240 	Linear Algebra 				3 cr
MATH 2275 	Calculus III 				4 cr
MATH 3326 	Elementary Analysis 			3 cr

The two courses, CS/ME 1165 Structured Programming and CS/ME 1166 Symbolic Programming, may be substituted for CS 1181.


    

    
Bachelor of Science in Mathematics

The Bachelor of Science program in Mathematics is designed to prepare
students to take
positions in industry, to pursue graduate training, or to enter the
teaching profession. It allows some flexibility in course work which
necessitates close cooperation with a mathematics department advisor
who should be selected early in the student's career. 

    

    Required Courses:
    
Mathematics Core (shown above) 				21 cr
MATH 2287       Foundations of Mathematics 		3 cr
MATH 3360       Differential Equations 			3 cr
MATH 4407       Modern Algebra  			3 cr
MATH 4423       Introduction to Real Analysis  		3 cr

    Plus one of the following courses:
    
MATH 3327       Vector Analysis 			3 cr
MATH 3343	Modern Geometry I			3 cr
MATH 3352 	Introduction to Probability 		3 cr
MATH 3362       Introduction to Complex Variables 	3 cr

    Plus 12 more credits of 4000-level mathematics coursework, which
includes completing two of the following sequences:
    
MATH 4407-4408  Modern Algebra 				6 cr
MATH 4423-4424  Introduction to Real Analysis 		6 cr
MATH 4441-4442  Introduction to Numerical Analysis 	6 cr
MATH 4450-4451  Mathematical Statistics 		6 cr




    
Bachelor of Science in Statistics

    The Bachelor of Science program in
Statistics is
designed to prepare students to take positions in industry or to pursue
graduate training. 
    
Required
Courses: (39 credits) 

    
Mathematics Core (shown above)				21 cr
MATH 3350	Statistical Methods			3 cr
MATH 3352	Introduction to Probability		3 cr
MATH 4450,4451	Mathematical Statistics I and II	6 cr
MATH 4457	Applied Regression Analysis		3 cr
MATH 4458	Experimental Design			3 cr

    
Additional
Courses: (9 credits)

    
A
student must take 9 additional credits from the
following list to complete the degree. With departmental approval, 3 of
the 9
credits may be completed by taking an appropriate advanced course
(4000-level)
in another field, such as Biology, Economics, etc. 

    
MATH 3360	Differential Equations			3 cr
MATH 4406	Advanced Linear Algebra  		3 cr
MATH 4423	Introduction to Real Analysis I  	3 cr
MATH 4424	Introduction to Real Analysis II	3 cr
MATH 4441	Introduction to Numerical Analysis I	3 cr
MATH 4442	Introduction to Numerical Analysis II	3 cr
MATH 4453	Topics in Statistics* 			3 cr
MATH 4459 	Applied Multivariate Analysis 		3 cr
*This is a 1-3 credit course, repeated for up to 3 credits

    

      

    

    


    

    
Associate of Science in Mathematics

Students seeking an Associate of Science degree in Mathematics must
complete the following:
    
General Education Goals for the 
  Bachelor of Science*                            variable

One of the two tracks described below. 

Track A is designed to provide the student with a broad overview 
of basic topics in mathematics. Track B is designed to provide the 
student with the lower-division coursework generally expected for 
a major or minor in mathematics.

    Track A
    
MATH 1123       Mathematics in Modern Society         3 cr
MATH 1127       The Language of Mathematics           3 cr
MATH 1130       Finite Mathematics                    3 cr
MATH 1144       Trigonometry**                        2 cr
MATH 1153       Introduction to Statistics            3 cr
MATH 1160       Applied Calculus                      3 cr
CS 1181         Introduction to Computer 
                  Science and Programming I           3 cr
TOTAL MATH CREDITS:                               20-22 cr

**MATH 1144 may be waived given a sufficient score on the Mathematics 
Placement Exam or the Mathematics Sub-test of the ACT or SAT.

    Track B
    
CS 1181         Introduction to Computer
                  Science and Programming I           3 cr
MATH 1170       Calculus I                            4 cr
MATH 1175       Calculus II                           4 cr
MATH 2275       Calculus III                          4 cr
MATH 2287       Foundations of Mathematics            3 cr
Approved MATH electives                               3 cr
TOTAL MATH CREDITS:                                  21 cr
Electives to bring total to 64 cr                 variable
                                              TOTAL: 64 cr

*The number of credits required for the General Education requirements 
varies depending on the student's performance on proficiency or placement 
tests in English, foreign languages, and mathematics.





    
Minor in Applied Mathematics

    
Required
courses:

    
Mathematics Core (shown above)			21 cr
MATH 3360      Differential Equations		 3 cr

    
Additional
courses: (3 credits)

    
Choose three
credits (one
course) from the following list:

    
MATH 3352	Introduction to Probability	3 cr
MATH 4421	Advanced 
		  Engineering Mathematics	3 cr
MATH 4441	Introduction 
		  to Numerical Analysis		3 cr
MATH 4465	Partial Differential Equations	3 cr

    

    


    

    
Minor in Mathematics

    Required Courses:
    
Mathematics Core (shown above)				21 cr 

    Additional courses (6 credits)

    
    
Choose six
credits (two courses) from the following list:

    
MATH 3327 	Vector Analysis 			3 cr
MATH 3343	Modern Geometry				3 cr
MATH 3352	Introduction to Probability		3 cr
MATH 3360       Differential Equations			3 cr
MATH 3362	Introduction to Complex Variables	3 cr
MATH 4407 	Modern Algebra I			3 cr
MATH 4408 	Modern Algebra II			3 cr
MATH 4423	Introduction to Real Analysis I		3 cr
MATH 4424	Introduction to Real Analysis II	3 cr
MATH 4444	Modern Geometry II			3 cr
MATH 4473	Introduction to Topology		3 cr




    
Minor in Statistics

    Required
Courses: (27 credits)
    
Mathematics Core (shown above)				21 cr
MATH 3350	Statistical Methods			3 cr
MATH 3352	Introduction to Probability		3 cr

    Additional
Courses: (3 credits)

    Choose 3 credits from
among
the following courses:

    
    
MATH 4450	Mathematical Statistics I 		3 cr
MATH 4451 	Mathematical Statistics II		3 cr
MATH 4453	Topics in Statistics* 			3 cr
MATH 4457	Applied Regression Analysis		3 cr
MATH 4458	Experimental Design			3 cr
MATH 4459	Applied Multivariate Analysis		3 cr

*This is a 1-3 credit course, repeated for up to 3 credits

    
    

    


    

    
Mathematics Courses

All mathematics courses except MATH 0015 have prerequisites. Students
place into a course either by completing the prerequisite courses with
a grade of C- or better (S in MATH 0015 and 0025) or by achieving
appropriate
scores on the ACT exam, SAT exam, or Compass mathematics placement
exam.
For placement purposes, prerequisite coursework or placement
examinations
must have been taken within the last seven years. See
the Mathematics Department for further information.
    
Students must pass a course with a grade of C- or better before
using that course as a prerequisite for another mathematics course.

    
MATH 0015 Arithmetic/Pre-algebra 0
credits
(3 credit equivalent). Arithmetic of integers and rational numbers.
Decimals; introduction to variables; linear equations; problems
involving rates,
ratios, proportions and percentages. Graded S/U. F, S, Su 

    
MATH 0025 Elementary Algebra 0 credits
(3
credit equivalent).
Variables and algebraic expressions. Absolute
value; linear equations and inequalities and their applications;
expansion and factorization of polynomials; rational expressions;
radical expressions; the real number line; the Cartesian coordinate
system and graphing of linear equations.
Graded S/U. PREREQ: S in MATH 0015, a Math ACT score of 16 or higher,
an SAT score of 390 or higher, or 46 or higher on the Pre-algebra
section (MAPL 1).
F, S, Su

    

    MATH 1108 Intermediate Algebra 3 Credits.
Topics in algebra, with an emphasis on solving equations and
inequalities. Systems of linear equations; quadratic equations and the
quadratic formula; polynomial, absolute value, rational, and radical
equations and inequalities. Radical
and  rational exponents. Parabolas,
distance formula and circles. PREREQ: S in MATH 0025, a Math
ACT score of 19 or higher, an SAT score of 460 or higher, or 45 or
higher on the algebra section
(MAPL 2). F,
S, Su 

    
MATH 1123 Mathematics in Modern
Society
3
credits.  Survey of applications of mathematics to real-world
problems. Topics from graph theory, management science, political
science, statistics, geometry, and computer science. PREREQ: MATH 0025.
Satisfies Goal 3 of the General Education Requirements. F, S, Su 

    
MATH 1127 The Language of Mathematics
3
credits.  Introduction to the precise language used throughout
mathematics. Development of skills including reading with
comprehension, expressing mathematical thoughts clearly, reasoning
logically, and employing common patterns of mathematical thought.
PREREQ: MATH 0025. Satisfies Goal 3 of the General Education
Requirements. S 

    
MATH 1130 Finite Mathematics 3
credits.  Introduction to probability, linear systems,
inequalities, and linear programming. Applications directed to
non-physical science areas. PREREQ: MATH 1108. Satisfies Goal 3 of the
General Education Requirements. F, S 

    
MATH 1143 College Algebra 3 credits. Functions
and their graphs. Notation, domain, range, composition, and inverses.
Basic transformations of graphs. Polynomial, rational, exponential, and
logarithmic functions and their graphs, with applications. Theory of
polynomial functions and equations. PREREQ: MATH 1108. F, S, Su 

    
MATH 1144 Trigonometry 2 credits. Circular
functions and right triangle approaches to trigonometry. Graphs of
trigonometric functions: amplitude, frequency, phase shift.
Trigonometric identities,
inverse functions, and equations. Introduction to vectors in the plane,
polar
coordinates, and polar representation of complex numbers. PREREQ: MATH
1143.
F, S, Su 

    
MATH 1147 Precalculus 5 credits. 
A single one-semester course equivalent to College Algebra (MATH 1143)
plus Trigonometry (MATH 1144). Credit cannot be granted in both MATH
1143
and MATH 1147, or in both MATH 1144 and MATH 1147. PREREQ: MATH 1108.
F, S

    
MATH 1153 Introduction to Statistics 3
credits.  Descriptive statistics, probability, confidence
intervals, and hypothesis testing for one and two parameters. Emphasis
on applications to a wide variety of disciplines. PREREQ: MATH 1108.
Satisfies Goal 3 of General Education Requirements. F, S, Su, W 

    
MATH 1160 Applied Calculus 3
credits. 
Course in differential and integral calculus designed primarily for
students in biological sciences, social sciences, business, education,
and humanities. Credit cannot be granted in both MATH 1160 and MATH
1170.
PREREQ: MATH 1143 or MATH 1147. Satisfies Goal 3 of the General
Education
Requirements.
F, S, Su 

    
MATH 1170 Calculus I 4 credits. First
course in the sequence 1170, 1175, 2275. Real-valued functions of
one real
variable: limits, continuity, derivatives, integrals, applications.
Credit
cannot be granted in both MATH 1160 and MATH 1170. PREREQ: MATH 1144 or
1147. Satisfies Goal 3 of the General Education Requirements. F, S,
Su 

    
MATH 1175 Calculus II 4 credits. 
Second course in the sequence 1170, 1175, 2275. Techniques of
integration,
trigonometric integrals, improper integrals. Applications of definite
integrals. First- and second-order linear differential equations with
constant coefficients. Sequences and series. Parametric curves in the
plane, polar coordinates. PREREQ: MATH 1170. F, S, Su

    
MATH 1187 Applied
Discrete Structures 3 credits.
Discrete structures in CS and EE. Boolean algebra and logic; sets,
functions, and relations; iteration, recursion, and induction;
algorithms; programming in pseudocode; basic counting principles;
graphs and trees; and other selected topics from discrete mathematics.
Cross-listed as CS 1187. PREREQ: CS 1181. S

    
 MATH 2240 Linear Algebra 3
credits. Introduction to linear
algebra. Linear systems, matrices,
determinants, vector spaces, linear transformations, linear
independence,
eigenvalues and eigenvectors, orthogonalization.
PREREQ: MATH 1170. F, S, Su 

    
MATH 2256 Structure of Arithmetic for
Elementary School Teachers 3 credits. Development of number
systems. Emphasis
on principles, representations, and concept development. For elementary
education majors. PREREQ: MATH 1143. F 

    
MATH 2257 Structure of Geometry and
Probability for Elementary School Teachers 3 credits. Topics from
geometry, probability, and statistics. Emphasis on principles,
representations, and concept development. For elementary education
majors. PREREQ: C- or
better in MATH 1143, MATH 1147, CET 1120, or
ELTR 1142, or one of the following: ACT > 26, SAT > 619, or pass
Math
Placement Exam Part C. S 

    
MATH 2275 Calculus III 4 credits. Third
course in the sequence 1170, 1175, 2275.  Multivariable calculus.
Vector
algebra and geometry. Functions of several variables. Differentiation.
Optimization. Multiple Integrals. Parametric curves and surfaces. Line
and surface integrals. Vector fields. Green's, Stokes', and divergence
theorems. PREREQ: MATH 1175. F, S 

    
MATH 2287 Foundations of Mathematics 3
credits. Logic and proofs, sets, functions, relations,
mathematical induction, and the cardinality of sets. PREREQ: MATH 1170.
F 

    
MATH 3326 Elementary Analysis 3
credits. A
beginning course in analysis on the real line.
Proof writing and the underlying logic are emphasized throughout the
course.
Topics include sets and functions, sequences, convergence, limits,
continuity,
and infinite series. PREREQ: MATH 1175 and either MATH 2240 or MATH 2287.
F, S 

    
MATH 3327 Vector Analysis 3 credits. Calculus
of vector functions of several variables, derivative matrix, chain
rule, inverse function theorem, multiple integration. Change of
variables. Integrals over curves and surfaces. Green's, Stokes' and
divergence theorems. Applications to physics. PREREQ: MATH 2275. F 

    
MATH 3343 Modern Geometry I 3 credits.
    Planar
Euclidian geometry. Rigid motions and symmetry in the plane. PREREQ:
MATH 2240 and MATH 2287. F 

    
MATH 3350
Statistical Methods 3 credits.
A calculus-based introduction to statistical procedures, including
simple regression, basic experimental design, and non-parametric
methods.  PREREQ: MATH 1160 or MATH 1170.
F, S

    
MATH
3352 Introduction to
Probability 3 credits. Fundamentals of probability,
discrete and
continuous random variables, distributions such as binomial, uniform,
Poisson,
hypergeometric, normal, gamma; expectation; joint, marginal,
conditional distributions;
central limit theorem; applications to statistics. Emphasizes material
needed
to develop statistical inference methods. PREREQ: MATH 1175 or
permission
of instructor. F, S 

    
MATH 3355 Operations Research 3
credits. Deterministic
problems in operations research oriented towards business. Includes
linear programming, transportation problems, network analysis, PERT,
dynamic programming, and elementary game theory. PREREQ: MATH 1130 or
MATH 2240, or permission
of instructor. AF 

    
MATH 3356 Operations Research II 3
credits. Probabilistic models oriented towards business are
treated. Selections from stochastic processes, Markov chains, queuing
theory, inventory theory, reliability, decision analysis and
simulation. PREREQ: MATH 3355. AS 

    
MATH 3360 Differential Equations 3
credits. Theory and applications of ordinary differential
equations. PREREQ: MATH 1175;  MATH 2275 recommended.
F, S 

    
MATH 3362 Introduction to Complex
Variables
3 credits. Introduction to the study of functions of a complex
variable including the algebra and geometry of complex numbers,
analytic functions, power series, integral theorems, and applications.
PREREQ: MATH 2275. D

    
MATH 4403
Survey of Combinatorics and Graph Theory 3 credits. Enumeration
techniques, including generating functions.
Applications. Introductory graph theory. PREREQ: MATH 1175 and MATH
2240. 

    
MATH 4404
Topics in Combinatorics and Graph Theory 3 credits. Continuation
of MATH 4403.
Application of algebraic, analytic, and/or probabilistic methods to
combinatorial, graph-theoretic, and algorithmic problems. PREREQ: MATH
4403 or
permission of instructor. D

    
MATH 4406 Advanced
Linear
Algebra 3 credits. Advanced linear algebra with a strong
emphasis on
proof.  Real and complex vector spaces,
linear
transformations, polynomials associated to matrices, determinants,
canonical
forms, inner product spaces. PREREQ: MATH 2240.  S

    
MATH 4407 Modern Algebra I 3 credits. Rings,
fields, groups, algebras, and selected topics in abstract algebra.
PREREQ: MATH 2240 and MATH 2287. F 

    
MATH 4408 Modern Algebra II 3 credits.
    Rings,
fields, groups, algebras, and selected topics in abstract algebra.
PREREQ: MATH 4407.  S 

    
MATH 4421 Advanced Engineering
Mathematics I 3 credits. Analysis of complex linear and nonlinear
engineering systems using advanced techniques, including Laplace
transforms, Fourier series
and classical partial differential equations. Cross-listed as ENGR
4421.
PREREQ: MATH 3360. F 

    
MATH 4422
Advanced Engineering Mathematics
II 3 credits. Analysis of complex linear and nonlinear engineering
systems using advanced techniques, including probability and
statistics, advanced numerical methods and variational calculus.
Cross-listed as ENGR 4422. PREREQ: ENGR 4421 or MATH 4421. S 

    
MATH 4423 Introduction to Real
Analysis
I
3 credits. The real number system, limits, sequences, series and
convergence; metric spaces; completeness; and selected topics on
measure and integration theory. PREREQ: MATH 2240, MATH 3326, and
MATH 3360. F 

    
MATH 4424 Introduction to Real
Analysis
II
3 credits. The real number system, limits, sequences, series and
convergence; metric spaces; completeness; and selected topics on
measure and integration theory. PREREQ: MATH 4423. S 

    
MATH 4435 Elementary Number Theory 3
credits. Diophantine equations, prime number theorems, residue
systems, theorems of Fermat and Wilson, and continued fractions.
PREREQ: MATH 4407. D 

    
MATH 4441 Introduction to Numerical
Analysis 3 credits. Introduction to numerical techniques for
solving problems dealing with nonlinear equations, systems of linear
equations, differential equations, interpolation, numerical
integration, and differentiation. PREREQ: MATH 2240, MATH 3326, and
MATH
3360 or permission of instructor. F 

    
MATH 4442 Introduction to Numerical
Analysis 3 credits. Extension of MATH 4441 for students who wish
to pursue more advanced techniques with emphasis on analysis. Typical
topics covered include numerical methods applied to partial
differential equations, integral equations, and in-depth treatment of
topics covered in MATH 4441. PREREQ: MATH 4441. S

    
MATH 4444 Modern Geometry II 3 credits.
Transformation groups. Topics from hyperbolic, projective, and other
geometries. S 

    
MATH 4450 Mathematical Statistics I 3
credits. Probability, random variables, discrete and continuous
distributions, order statistics, limit theorems, point and interval
estimation, uniformly most powerful tests, likelihood ratio tests,
chi-square and F tests, nonparametric tests. PREREQ: MATH 3326. F 

    
MATH 4451 Mathematical Statistics II 3
credits. Probability, random variables, discrete and continuous
distributions, order statistics, limit theorems, point and interval
estimation, uniformly most powerful tests, likelihood ratio tests,
chi-square and F tests, nonparametric tests. PREREQ: MATH 4450. S

    
MATH
4453 Topics in Statistics 1-3 credits. Content varies. May be
repeated for up to
6 credits. PREREQ: Permission of instructor. D

    
MATH 4457 Applied Regression Analysis
3
credits. Simple and multiple linear regression, polynomial
regression, diagnostics, model selection, models with categorical
variables. PREREQ: MATH 3350 or MATH 3352 or
permission of instructor. D 

    
MATH 4458 Experimental Design 3
credits.
The linear model for experimental designs, analysis of variance and
covariance, block designs, factorial designs, nested designs, choice of
sample size. PREREQ: MATH 3350 or MATH 3352 or permission of
instructor. D 

    
MATH 4459 Applied
Multivariate Analysis 3
credits. Matrix computation of summary statistics, graphical
analysis of multivariate procedures, multivariate normal distribution,
MANOVA, multivariate linear regression, principal components, factor
analysis, canonical correlation analysis. PREREQ:  MATH 2240 and one of the
following: MATH 3350, MATH 4457, MATH 4458, or permission of instructor.
D 

    
MATH 4465 Partial Differential
Equations
3
credits. Equations of the first and second orders, methods of
solution,
Laplace's equation, heat equation, and wave equation. Emphasis on
applications
in physical sciences and engineering. PREREQ: MATH 2275 and MATH 3360.
D 

    
MATH 4473 Introduction to Topology 3
credits. Metric spaces; convergence; notions of continuity;
connected, separable and compact spaces. PREREQ: Permission of
instructor. D 

    
MATH 4481 Directed Readings and
Problems
1-3 credits. Individual
work under the direction of a professor. May be repeated for up to 6
credits.  PREREQ: Senior or graduate
student in good standing. D

    
MATH 4491 Mathematics Seminar 1-3
credits. Advanced reading and discussion on selected topics in
mathematics.
May be repeated. PREREQ: 90 credits or equivalent. D

  











  
    

      
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