# Mathematics (MATH)

*For placement in college mathematics courses see Arts and Sciences—Mathematics and Logic Requirement—Placement. Due to the sequential nature of the study of mathematics, once students have received credit for, or established proficiency at, one level in a sequence of mathematics coursework, they are not allowed to receive academic credit toward graduation for a prior course in the sequence or for a course in a lower sequence. Students with questions concerning the applicability of such sequential coursework should consult the Department of Mathematical Sciences.
*

**10006 Core Mathematics I and II (4)**

Covers exactly the same topics as MATH 10021 and 10022 combined. Not offered on every campus. Hours do not count toward graduation. Prerequisite: none. Special fee: $22.50 flat fee—subject to change.

**10007 Core Mathematics III and IV (4)**

Covers exactly the same topics as MATH 10023 and 10024 combined. Not offered on all campuses. Students should have appropriate placement scores, or have a minimum C (2.0) grade in MATH 10022 or MATH 10006 before taking this class. Prerequisite: none. Special fee: $22.50 flat fee—subject to change.

**10020 Pre-Core Mathematics (2)
**Properties of whole numbers, fractions, decimals, percents, signed numbers and order of operations, to a greater degree than in Core Math I and Core Math II. Mental math and elementary algebraic theinking skills are emphasized and calculators are not allowed. Hours do not count toward graduation. Prerequisite: none.

**10021 Core Mathematics I (2)
**Includes operations on integers, fractions, decimals and percents, properties of real numbers. Introduction to variables, first degree equations and problem-solving with formulas. Equations and inequalities in one variable, linear equations, rate of change and slope, graphing in the Cartesian plane. Hours do not count toward graduation. Prerequisite: none. Special fee: $22.50 flat fee—subject to change.

**10022 Core Mathematics II (2)**

Introduction to functions, systems of linear equations, exponents, polynomial operations, scientific notation. Factoring polynomials, solving quadratics by factoring, radicals and rational exponents. Hours do not count toward graduation. Students should have appropriate placement scores, or have a minimum C (2.0) grade in MATH 10021 before taking this class. Prerequisite: none. Special fee: $22.50 flat fee—subject to change.

**10023 Core Mathematics III (2)
**Zeros of functions, rational expressions and equations, problem-solving with rational expressions, intermediate factoring techniques. Quadratics: functions, graphs, equations, inequalities, "quadratic type" equations and problem-solving. Prerequisite: none. Students should have appropriate placement scores, or have a minimum C (2.0) in MATH 10006 or 10022 before taking this class. Special fee: $22.50 flat fee—subject to change.

**10024 Core Mathematics IV (2)**

Advanced factoring techniques, rational functions, radical equations, absolute value equations and inequalities. Exponential and logarithmic functions: introduction, graphing, problem-solving. Prerequisite: none. Students should have appropriate placement scores, or have a minimum C (2.0) in MATH 10023 before taking this class. Special fee: $22.50 flat fee—subject to change.

**10041 Elementary Probability and Statistics (3)
**Descriptive statistics, probability concepts, binomial and normal distributions. Sampling, estimation, hypothesis testing. Analysis of paired data, linear models and correlation. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Students should have appropriate placement scores, or have a minimum C (2.0) grade in MATH 10007 or any math course numbered MATH 10023 or higher before taking this class. Prerequisite: none.

**11008 Explorations in Modern Mathematics (3)**

Topics from various branches of mathematics are chosen to introduce student to the wide varieties of ways in which mathematics affects everyday life. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Students should have appropriate placement scores (at least ACT 22 or equivalent), or have a minimum C (2.0) grade in MATH 10007 or any math course numbered MATH 10023 or higher before taking this class. Prerequisite: none. This course may be used to satisfy the Kent Core.

11009 Modeling Algebra (4)

Study of algebra arising in the context of real-world applications, including linear, polynomial, exponential and logarithmic models. Intended for students not planning to take calculus. No credit for MATH 11010. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Students may not earn credit for this class if they have previously earned credit for MATH 11010. Students should have appropriate placement scores (at least ACT 22 or equivalent), or have a minimum C (2.0) grade in MATH 10023 or MATH 10007 before taking this class. Prerequisite: none. This course may be used to satisfy the Kent Core.

**11010 Algebra for Calculus (3)**

Study of elementary functions and graphs, including polynomial, exponential and logarithmic functions; complex numbers; binomial theorem. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Student should have appropriate placement scores (at least ACT 22 or equivalent), or have a minimum C (2.0) grade in MATH 10024 or MATH 10007 before taking this class. Prerequisite: none. This course may be used to satisfy the Kent Core.

**11012 Intuitive Calculus (3)**

Designed to give an overview of differential and integral calculus to business and life science majors. Does not include trigonometric functions. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Students should have appropriate placement scores, or have minimum C (2.0) grade in MATH 11010 before taking this class. Prerequisite: none. This course may be used to satisfy the Kent Core.

**11022 Trigonometry (2)
**Solution of triangles, trigonometric equations and identities. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Students should have appropriate placement scores, or take MATH 11010 concurrently, or have a minimum C (2.0) grade in MATH 11010 before taking this class. Prerequisite: none.

**12002 Analytic Geometry and Calculus I (5)**

Concepts of limit, continuity and derivative, and the indefinite and definite integral for functions of one real variable. Maximization, related rates, fundamental theorem of calculus. No credit for MATH 12011 or 12012. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Prerequisite: a grade of C (2.0) or better in MATH 11010 and 11022. This course may be used to satisfy the Kent Core.

**12003 Analytic Geometry and Calculus II (5)**

Continued study of techniques and applications of integration; trigonometric, logarithmic and exponential functions; polar coordinates; vectors; parametric equations; sequences and series. Prerequisite: MATH 12002 or 12012.

**12011 Calculus with Precalculus I (3)**

Introduction to differential calculus with a review of algebra and trigonometry. Includes exponents, factoring, functions, graphs, tangent lines, limits, continuity, derivatives and related rates. No credit for MATH 12002. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Prerequisite: Compass Algebra score of 55 or better with either an SAT Math score of at least 480 or an ACT Math score of at least 20; or Compass Algebra score of 36 or better with either an SAT Math score of at least 620 or an ACT Math score of at least 27. This course may be used to satisfy the Kent Core.

**12012 Calculus with Precalculus II (3)**

Development of integral calculus and continued study of differential calculus. Includes curve sketching, optimization, fundamental theorem of calculus, areas between curves, exponential and logarithmic functions. No credit for MATH 12002. Prerequisite: MATH 12011. This course may be used to satisfy the Kent Core.

**12021 Calculus for Life Sciences (4)**

Differential and integral calculus using examples and problems in life sciences. Prerequisite: integrated life sciences (ILS) major.

**12022 Probability and Statistics for Life Sciences (3)**

Probability and statistics with applications in medical and biological sciences. Prerequisite: MATH 12021 or 12003.

**14001 Basic Mathematical Concepts I (4)**

Development of the real number system and its sub-systems, open sentences, numeration systems, modular arithmetic and some number theory concepts. Students who have not taken a previous mathematics course at Kent State must see an academic advisor for placement. Prerequisite: none. Student should have appropriate placement scores (at least ACT 22 or equivalent), or have a minimum C (2.0) grade in MATH 10007 or any math course numbered higher than MATH 10023 before taking this class.This course may be used to satisfy the Kent Core.

**14002 Basic Mathematical Concepts II (4)**

Basic concepts of probability, statistics and geometry. Prerequisite: MATH 14001. This course may be used to satisfy the Kent Core.

**19001 Technical Mathematics I (4)****

Introduction to geometry, algebra and trigonometry. For students in the engineering technologies. Prerequisite: special approval.

**19002 Technical Mathematics II (4)****

Continuation of MATH 19001. Emphasizes advanced topics in algebra and trigonometry, analytic geometry, derivatives and integrals. Prerequisite: MATH 19001.

**19099 Field Experience in Mathematics Instruction (1)***

(Repeatable for credit) Learning through tutoring. A supervised laboratory experience in providing explanations of mathematical concepts. May be repeated in a different area. Prerequisite: special approval.

**20095 Special Topics in Mathematics (1-5)***

(Repeatable for credit) Various special courses will be announced in the Schedule of Classes under this course number with different section numbers. Prerequisite: special approval.

**21001 Linear Algebra with Applications (3)**

Systems of linear equations and the associated matrix operations, linear transformations, vector spaces, bases, eigenvectors. Prerequisite: MATH 11012 or 12002.

**21003 Introduction to Systems Analysis and Data Communications (3)****

(Cross-listed with COMT 21003) Background in the topic of systems analysis, design, development and implementation including an overview of teleprocessing. Prerequisite: MIS 24080.

**21092 Computer Practicum (2)* ****

(Repeatable for credit) (Cross-listed with COMT 21092) Supervised work experience in a computer installation. Prerequisite: none.

**22005 Analytic Geometry and Calculus III (3)**

Study of functions of several variables, including partial derivatives and multiple integrals. Prerequisite: MATH 12003.

**23022 Discrete Structures for Computer Science (3)**

(Cross-listed with CS 23022) Discrete structures for computer scientists with a focus on: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, applications and modeling. Specific topics include logic, sets, functions, relations, algorithms, proof techniques, counting, graphs, trees, Boolean algebra, grammars and languages. No credit for MATH 31011. Prerequisites: CS 10051 and a grade of C (2.0) or better in MATH 11010 or 11011 and 11022; or a Compass Algebra score of 55 or better and either SAT Math score of 540 or better or ACT Math score 23 or better.

**30011 Basic Probability and Statistics (3)**

Analysis and representation of data. Controlled experiments and observations. Measurement errors. Correlation and regression. Sampling. Probability models and tests of models. Inference. Prerequisite: a grade of C (2.0) or better in MATH 11010 or 11011 or 12001.

**30055 Mathematical Theory of Interest (3)**

A calculus-based introduction to the mathematics of finance. Limited to deterministic analysis of interest rates, annuities, bonds and immunization. Emphasizes the mathematical theory of the subject matter. Prerequisite: MATH 12003.

**31011 Discrete Mathematics (3)**

Discrete mathematical techniques and structures including finite set theory, graph theory, propositional calculus, combinatorics and discrete probability. Formal methodology and proof techniques. Prerequisites: MATH 12002. Pre/corequisite: MATH 21001.

**31045 Formal Logic (3)**

(Cross-listed with CS 31045 and PHIL 31045) Study of first-order predicate calculus with identity and function symbols. Prerequisite: none.

**32044 Introduction to Ordinary Differential Equations (3)
**An introduction to ordinary differential equations and applications. Topics include solution methods, series solutions and singular points. Laplace transforms and linear systems. Applications include population dynamics, forced oscillations and resonance. Prerequisites: MATH 21001 and 22005.

**32051 Mathematical Methods in the Physical Sciences I (4)**

Mathematics background beyond Calculus I and II for upper-division courses in the physical sciences. Topics include complex numbers and arithmetic, linear algebra, partial differentiation and multiple integrals. Prerequisite: MATH 12003.

**32052 Mathematical Methods in the Physical Sciences II (4)**

Additional mathematics background for upper-division courses in the physical sciences. Topics include vector analysis, Fourier series and transforms, ordinary differential equations and partial differential equations. Prerequisite: MATH 32051; or 21001 and 22005.

**34001 Fundamental Concepts of Algebra (3)**

Professionalized course in algebra for prospective secondary teachers. Postulational development of number system of algebra; other systems, related topics, applications. Prerequisite: MATH 12002.

**34002 Fundamental Concepts of Geometry (3)**

Professionalized course in geometry for secondary school teachers. Origin and development of the geometry of Euclid with modern refinements, topics, approaches. Other geometries, applications. Prerequisite: MATH 12002.

**40011 Introduction to Probability Theory and Applications (3)**

Permutations and combinations, discrete and continuous distributions, random variables, conditional probabilities, Baye’s formula, mathematical expectation, law of large numbers, normal approximations, basic limit theorems. Prerequisite: MATH 12003.

**40012 Introduction to Statistical Concepts (3)**

Sample spaces, continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, types of error, level and power of tests, sequential and nonparametric methods. Prerequisite: MATH 40011.

**40022 Linear Models and Statistical Analysis (3)**

Regression model, multivariate normal distribution, point and interval estimates, Gauss-Markov Theorem, correlation and regression, tests of hypotheses, applications. Prerequisites: MATH 21001 and 40012.

**40031 Basic Nonparametric Statistics (3)**

Rank tests for different kinds of hypothesis, large sample theory, efficiency comparisons, tests of Kolmogorov-Smirnov type. Prerequisite: MATH 40012.

**40041 Statistical Methods for Experiments (3)**

Comparison of two groups, t- and F-statistics, ANOVA, one-way and multiway layouts, randomization, blocking. Linear regression, correlation and analysis of covariance (ANCOVA). Repeated measures analysis of variance. Prerequisites: MATH 30011.

**40042 Sampling Theory (3)**

This introductory course provides the methodology for the design and analysis of sampling and surveying studies. Simple random, stratified, cluster, PPS and two-stage sampling techniques. Linear, ratio and regression estimators. Prerequisite: MATH 30011.

**40051 Topics in Probability Theory and Stochastic Processes (3)**

Topics from conditional expectations, Markov chains, Markov processes, Brownian motion and Martingales and their applications to stochastic calculus. Prerequisite: MATH 40011.

**40055 Actuarial Mathematics I (4)**

Topics from survival models, stochastic analysis of annuities and life insurance and casualty models. Prerequisite: MATH 30055 and 40011.

**40056 Actuarial Mathematics II (4)**

Benefit premiums, benefit reserves and their analysis; decrement models, joint survivorship, risk models. Prerequisite: MATH 40055.

**40091 Seminar in Actuarial Mathematics (2)**

(Repeatable for credit) Seminar course designed to prepare students for the Society of Actuaries examination on actuarial mathematics. Prerequisite: MATH 40056.

**40093 Variable Title Workshop in Mathematics (1-6)**

(Repeatable for credit) Studies special topics in mathematics. Not acceptable for credit toward a major or minor in math without approval of student’s advisor. S/U grading. Prerequisite: special approval.

**41001 Introduction to Modern Algebra I (3)**

Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains, and homomorphisms. Prerequisites: MATH 21001 and 22005. This course may be used to satisfy the writing-intensive requirement with approval of major department.

**41002 Introduction to Modern Algebra II (3)**

A continuation of MATH 41001, emphasizing properties of rings, their ideals, polynomial ring extensions, fields, finite degree extensions, roots of polynomials, constructability. Prerequisite: MATH 41001. This course may be used to satisfy the writing-intensive requirement with approval of major department.

**41012 Finite Mathematics (3)**

(Cross-listed with CS 41012) A continuation of Discrete Math, emphasizing combinatorial techniques, graph applications in algorithms, finite algebra, number theory and probability. Covers useful math for CS majors. Prerequisite: CS 31011 or MATH 31011.

**41021 Theory of Matrices (3)**

A rigorous study of the topics introduced in matrix algebra. Topics included are vector space preliminaries, canonical forms of matrices, diagonalizability criteria. Prerequisites: MATH 21001 and 22005.

**41045 Metalogic (3)**

(Cross-listed with CS 41045 and PHIL 41045) May be counted toward B.A. or B.S. in mathematics major. See PHIL 41045 for description. Prerequisite: PHIL 31045.

**42001 Introduction to Analysis I (3)**

Topics include basic structure of the real numbers, Cauchy sequences, convergence, completeness of the real numbers, continuity, differentiation and Riemann integration. Prerequisites: MATH 21001 and 22005. This course may be used to satisfy the writing-intensive course requirement with approval of major department.

**42002 Introduction to Analysis II (3)**

Topics include further development of integration theory, infinite series, uniform convergence, several variable calculus and metric spaces. Prerequisite: MATH 42001. This course may be used to satisfy the writing-intensive course requirement with approval of major department.

**42011 Mathematical Optimization (3)**

Analytic and numerical techniques for location of extreme points of functions and calculus of variations. Both constrained and unconstrained problems are considered. Prerequisites: MATH 21001 and 22005.

**42021 Graph Theory and Combinatorics (3)**

Fundamentals and applications of combinatorial mathematics. Topics include traversability, colorability, networks, inclusion and exclusion, matching and designs. Prerequisites: MATH 12003 and 21001.

**42024 Numbers and Games (3)**

The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory. Prerequisite: MATH 21001.

**42031 Mathematical Models and Dynamical Systems (3)**

Formulation and analysis of mathematical models for a variety of phenomena. Mathematical methods from optimization, dynamical systems and probability are developed and applied. Modern software tools are utilized. Prerequisite: MATH 32044.

**42041 Advanced Calculus (3)**

The calculus and applications of scalar and vector functions of several variables. Vector differential and integral calculus. Applications to field theories, electricity and magnetism, and fluid flow. Prerequisites: MATH 21001 and 22005.

**42045 Introduction to Partial Differential Equations (3)**

An introduction to Fourier series, Fourier transforms and partial differential equations. Wave, heat and potential equations of mathematical physics. Additional topics include Green’s functions and the Method of Characteristics for wave equations. Prerequisite: MATH 32044.

**42048 Introduction to Complex Variables (3)
**Algebra of complex numbers, analytic functions, mappings, Cauchy integral theory, residue theory and applications. Prerequisite: MATH 22005.

**42091 Seminar: Modeling Projects (3)**

(Repeatable for credit) Individual and small-group projects concerned with the formulation and analysis of mathematical models in a variety of areas. Written and oral reports are required. IP grade permissible. Prerequisite: MATH 42031. This course may be used to satisfy the writing-intensive course requirement with approval of major department.

**42201 Introduction to Numerical Computing I (3)**

(Cross-listed with CS 42201) An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-square data fitting, nonlinear equations and systems, and optimization problems. Prerequisites: MATH 12003 and 21001 and CS 23021. Special fee: $10 flat fee—subject to change.

**42202 Introduction to Numerical Computing II (3)**

(Cross-listed with CS 42202) A continuation of MATH 42201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Prerequisites: MATH 32044 and 42201. Special fee: $10 flat fee—subject to change.

**45011 Differential Geometry (3)**

Analytic and metric differential geometry of curves and surfaces. Prerequisite: MATH 22005.

**45021 Euclidean Geometry (3)**

Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles; cross-ratio, groups, constructions, geometric generalizations; inversion. Prerequisite: MATH 21001 or special approval of instructor.

**45022 Linear Geometry (3)**

Using transformations as a tool to study geometry and to differentiate between different kinds of geometry. Linear algebra methods applied to geometry. Prerequisite: MATH 21001.

**46001 Elementary Topology (3)**

Metric spaces, introduction to topological spaces, separation axioms. Prerequisite: MATH 22005.

**47001 Mathematical Logic and Set Theory (3)**

Axiomatic set theory, relations, development of real numbers, cardinal numbers, axiom of choice. Prerequisite: special approval.

**47011 Theory of Numbers (3)**

Divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations. Prerequisite: MATH 12003.

**47021 History of Mathematics (3)**

Survey from Babylonian and Egyptian mathematics to 20th century mathematics with emphasis on the development of algebra, geometry, calculus, number theory. Prerequisite: 3 credit hours of mathematics beyond 22005.

**49995 Selected Topics in Mathematics and Its Applications (1-4)**

(Repeatable for credit) Various special courses will be announced in the Schedule of Classes under this course number with different section numbers. Prerequisite: special approval.

**49996 Individual Study (1-4)**

(Repeatable for credit) Prerequisite: special approval of instructor.

**49998 Research (1-15)**

(Repeatable for credit) Prerequisite: special approval.

* *Course ineligible to be repeated for GPA recalculation.
**Courses offered only at Regional Campuses.*

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