Mathematics Courses

MATH 050

Math Workshop

0 credit hours

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MATH 105

Liberal Arts Mathematics

3 credit hours

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This course is designed to increase an awareness of and an appreciation for mathematics as a mode of non-literary communication. The student will be introduced to topics selected from, but not limited to: algebra, geometry, calculators and computers, probability and statistics, the mathematics of social choice, management science, growth and symmetry and the mathematics of finance. NOTE: Credit hours CANNOT be earned for this course if the student is concurrently enrolled or has previous credit for any mathematics course numbered above 105. Offered fall and spring.

MATH 110

Geometry for Art and Design

3 credit hours

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This course will develop students' quantitative reasoning skills through exploration of geometric measurement, formulas, and visualization in 2D and 3D. Topics include mathematical representation, interpreting models, drawing inferences, estimating for reasonableness, finding patterns, proving generalizations. Work of relevant artists will be studied to make connections with geometric concepts. Offered fall.

MATH 112

College Algebra

3 credit hours

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Topics for this course include a problem-solving approach to the study of polynomial, rational, exponential and logarithmic functions, graphs, models, complex numbers, and conic sections. The graphing calculator is an integral part of this course. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall, spring and summer.

MATH 113

Trigonometry

3 credit hours

P: MATH-112 with a grade of C or better
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Topics for this course include trigonometric functions and their inverses, identities, trigonometric equations, formulas and solving triangles. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall, spring and summer.

MATH 120

Special Topics: History of Math

3 credit hours

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This course provides a comprehensive exploration of the historical development of mathematics, spanning ancient civilizations to the modern era. Through an interdisciplinary approach, students will delve into the evolution of mathematical ideas, the contributions of key mathematicians, and the cultural, societal, and scientific contexts that shaped mathematical thought.

MATH 121

Mathematics Content for ElementaryýTeachers I

3 credit hours

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This course explores the underlying structure and basis for the mathematics taught in elementary school. Topics include functions, patterns and problem solving, numeration, operations on natural numbers, whole numbers and integers, rational numbers, number theory, and fraction models and operations. Offered fall.

MATH 122

Mathematics Content for ElementaryýTeachers II

3 credit hours

P: MATH-121 with a grade of C or better
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This course explores the underlying structure and basis for the mathematics taught in elementary and middle school. Topics include rational and irrational numbers, real numbers, measurement, geometry and probability. Offered spring.

MATH 131

Finite Mathematics

3 credit hours

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Topics for this course include review of linear equations and inequalities, mathematics of finance, introduction to linear programming, set theory, counting techniques, and permutations and combinations. The TI-83 plus or TI-84 plus graphing calculator is required. NOTE: Credit will not be granted for both MATH 131 and MATH 200.

MATH 132

Business Statistics

4 credit hours

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Topics for this course include collecting, organizing, analyzing and interpreting data with an emphasis on business applications, descriptive statistics, sampling, probability, probability distributions, estimation, hypothesis testing, introduction to linear regression, and correlation analysis. Excel software is used throughout the course. The TI-83 plus or TI-84 plus graphing calculator is required. NOTE: Credit will not be granted for both MATH 132 and MATH 135.

MATH 135

Introduction to Statistics

4 credit hours

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Topics for this course include collecting, organizing, analyzing and interpreting data with emphasis on a wide range of applications, descriptive statistics, sampling, probability, probability distributions, estimation, hypothesis testing, introduction to linear regression, and correlation analysis. Microsoft Office Excel is used throughout the course. Offered fall, spring and summer.

MATH 150

Special Topics: Geometry for Art andýDesign

3 credit hours

P: Math-095
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This course will develop students' quantitative reasoning skills through exploration of geometric measurement, formulas and visualization in 2D and 3D. Topics include: representing mathematical information symbolically, visually, numerically, and verbally; interpreting mathematical models such as formulas and figures; drawing inferences; estimating problems for reasonableness, finding patterns, proving generalizations. Work of relevant artists will be used to make connections with geometric concepts. Technology tools used: dynamic geometry and vector graphic software, 3D printer, laser cutter. Offered fall.

MATH 150

Special Topics: Principles of CollegeýAlgebra

3 credit hours

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The course will cover algebraic principles at an intermediate level. Content includes real and complex numbers, polynomials, factoring, radicals, rational expressions, quadratic equations, and an introduction to functions including exponential and logarithmic functions. Specific focus will be given to topics needed in order to be successful in their future Saint Xavier courses.

MATH 188

Statistics

3 credit hours

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MATH 200

Introduction to Discrete Mathematics

3 credit hours

P: MATH-112 with a grade of C or better or placement
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Topics for this course include number systems, set theory, logic, methods of proof, combinatorics, relations and functions, algorithms, recursion, and the Fibonacci sequence. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall and spring.

MATH 201

Calculus with Analytic Geometry I

4 credit hours

C: MATHL-201
E: MATH-200
P: MATH-113 with a grade of C or better or placement

Topics for this course include review of: algebraic and trigonometric functions and their graphs, absolute value and inequalities, the concepts of limit and continuity, theory and techniques of differentiating algebraic and trigonometric functions and applications of differentiation. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall and spring.

MATHL 201

Calculus Lab

0 credit hours

C: MATH-201
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MATH 202

Calculus with Analytic Geometry II

4 credit hours

C: MATHL-202
P: MATH-201 with a grade of C or better
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Topics for this course include: derivatives and integrals of transcendental functions, indeterminate forms, improper integrals, techniques and applications of integration. Time permitting: numerical integration, conic sections, parametric equations and polar coordinates will be covered. The TI-83 plus or TI-84 plus graphing calculator is required. Offered spring.

MATHL 202

Calculus Lab

0 credit hours

C: MATH-202
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MATH 203

Calculus with Analytic Geometry III

4 credit hours

P: MATH-202 with a grade of C or better
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Topics for this course include: vectors and vector calculus, analytic geometry in three-space, differentiation of functions of several variables, multiple integration and applications. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall.

MATH 211

Linear Algebra

4 credit hours

E: MATH-202
P: MATH-200 with a grade of C or better
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This course includes elementary concepts of linear algebra, systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors and applications. The TI-83 plus or TI-84 plus graphing calculator is required. Offered spring.

MATH 301

Advanced Calculus

4 credit hours

P: MATH-202 with a grade of C or better
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Topics for this course include: convergence, sequences, indeterminate forms, improper integrals, infinite series, Taylor and Fourier Series, applications, functions defined by integrals, the gamma and beta functions. The TI-83 plus or TI-84 plus graphing calculator is required. Offered spring.

MATH 303

Differential Equations

3 credit hours

C: MATH-301
P: MATH-202 with a grade of C or better
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Topics for this course include: differential equations of first order, second order and higher order linear differential equations, non-homogeneous equations; power series solutions to linear differential equations, numerical methods for solving linear and nonlinear differential equations. The TI-83 plus or TI-84 plus graphing calculator is required. Offered as needed, spring.

MATH 305

Probability and Statistics I

3 credit hours

P: MATH-203 MATH-301 with a grade of C or better
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Topics for this course include: exploratory data analysis, geographical techniques, measures of central tendency and variability, concepts of probability, Bayes' Rule, Expected Value, discrete distributions, continuous distributions, moment generating functions, and joint probability densities. The statistical software R is used throughout the course. The TI-83 plus or TI-84 plus graphing calculator is required. Offered fall.

MATH 306

Probability and Statistics II

3 credit hours

P: MATH-305 with a grade of C or better
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This course is a continuation of MATH 305 concerned with sampling distributions, confidence intervals and hypothesis testing (one sample, two sample, means, proportions, variances, chi-square), linear regression and correlation, with an emphasis on both theory and applications. The statistical software R is used throughout the course. The TI-83 plus or TI-84 plus graphing calculator is required. Offered spring.

MATH 307

Modern Geometry

3 credit hours

P: MATH-202 with a grade of C or better,ENGL-120
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Topics for this course include: the foundations of geometry as a mathematical system, elementary logic, advanced constructions, historical background and basic concepts of finite and infinite Euclidean and non-Euclidean geometries; cross ratio, affine and projective planes; the theorems of Ceva, Menelaus, Desargues, Pascal and Pappus. Offered as needed, fall.

MATH 308

History of Mathematics

3 credit hours

P: MATH-202 with a grade of C or betterENGL-120
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This course provides historical perspective of the development of mathematics with emphasis on the multicultural dimension from ancient to modern times. Students will do problems in the methods of the ancients and compare to modern solutions and learn to appreciate mathematics as a product of human effort. Historical development of calculus and other modern mathematical areas will be studied. Offered as needed, spring.

MATH 309

Abstract Algebra I

3 credit hours

P: MATH-211 with a grade of C or better
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Topics for this course include: integers, groups, subgroups, cosets, homomorphisms, permutation groups, rings, subrings, integral domains and fields. Offered as needed, fall.

MATH 313

Partial Differential Equations

3 credit hours

P: MATH-203 with a grade of C or betterMATH-303 with a grade of C or better
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Topics for this course include: Partial differential equations of first order and second order, heat equations, wave equations, Laplace equations in one and in higher dimensions, homogeneous and inhomogeneous cases, and applications. Offered as needed.

MATH 314

Integral Equations

3 credit hours

P: MATH-202 with a grade of C or better
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Topics for this course include: Fredholm integral equations, Volterra integral equations, Integro-differential equations, Singular integral equations, First and second kind integrals. Offered as needed.

MATH 315

Numerical Analysis

3 credit hours

P: MATH-202 with a grade of C or better
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Topics for this course include: iterative solutions to non-linear equations, Newton-Raphson and secant methods, numerical solutions of ODEs, numerical integration methods, interpolation and curve fitting. The TI-83 plus or TI-84 plus graphing calculator is required. Offered as needed.

MATH 321

Discrete Methods

3 credit hours

P: Math-200 with a grade of C or better
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Topics for this course may include some of the following: Euler and Hamilton circuits, graph coloring, matching theory, applied combinatorics, mathematical induction, equivalence relations and congruence classes, recurrence relations, generating functions and applications. Offered fall.

MATH 331

Theory of Interest

3 credit hours

P: MATH-202 with a C or better
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Topics for this course include: compound interest, annuities, bonds, measurement of mortality, life annuities, life insurance, premiums and reserves. A financial calculator is required for this course. Offered as needed.

MATH 336

Real Analysis

3 credit hours

P: MATH-301 with a grade of C or better
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This course is intended to deepen and broaden students' knowledge of the theory of calculus. Topics for this course include: properties of real numbers, sequences and series, continuity, differentiation, integration, metric spaces and topology. Offered as needed.

MATH 350

Selected Advanced Topics in MathematicsýEducation

1 credit hour

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Courses offered on an occasional basis devoted to select advanced mathematical education topics. Offered as needed.

MATH 351

Methods of Teaching Middle Levelý(Grades 5-8) Mathematics

3 credit hours

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Focal points include principles, standards, current issues, implications of research, and resources and instructional methods related to the teaching and learning of middle level (grades 5-8) mathematics. Offered as needed.

MATH 360

Selected Topics in Advanced Mathematics

1 credit hour

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Possibilities include: real analysis; complex analysis; number theory; topology; transform methods; partial differential equations; integral equations, Abstract Algebra II; Differential Geometry. Prerequisite: See the division director. Offered as needed.

MATH 360

SpTop:Number Theory

3 credit hours

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Possibilities include: Real Analysis; Complex Analysis; Number Theory; Topology; Transform Methods; Partial Differential Equations; Integral Equations, Abstract Algebra II; Differential Geometry. Offered at least once each academic year.

MATH 360

Special Topics: Cryptography

3 credit hours

P: Take Math-200 AND CMPSC-112
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This course provides an introduction to cryptography and its applications. A survey of classical ciphers, private and public key cryptosystems, and hashing algorithms will be discussed. Previous knowledge of matrix operations and simple algorithms is required. Graduate students will be expected to complete a project in an advanced programming language.

MATH 375

Methods of Teaching Mathematics, Gradesý9-12

3 credit hours

P: at least 30 hours in the mathematics major
P: MATH-301
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Focal points include: principles, standards, current issues, implications of research, and resources and instructional methods related to the teaching and learning of secondary (grades 9-12) mathematics. 30 clinical hours. Offered fall.

MATHL 375

Secondary Mathematics edTPA Workshop

0 credit hours

C: MATH-375
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Students will complete activities for Task 1 Planning for Mathematics Instruction and Assessment, Task 2 Instructing and Engaging Students in Learning, and Task 3 Assessing Student Learning. Topics include: lesson planning for a learning segment, development of assessments, analysis of mathematical language and facilitation of conceptual understanding, procedural fluency, mathematical reasoning and problem-solving skills in the mathematics classroom. Offered as needed.

MATH 390

Internship

1 credit hour

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For students who perform internships and/or present an off-campus experience judged by the faculty advisor and division director to be of significant value in mathematical studies. Offered as needed.

MATH 399

Senior Seminar

1 credit hour

P: Senior standing and program consent
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The purpose of the Senior Seminar is to provide a culminating experience in mathematics for Mathematics majors; and Mathematics with Secondary Education majors. The student will conduct research on an advanced topic with guidance from a faculty member, prepare a paper, prepare a poster and give a presentation based on the research to faculty and students of the program. The student is expected to attend all presentations given during the semester. Offered as needed, fall.

MATHL 399

Senior Seminar Lab

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Lab for Math Senior Seminar.