School of Arts and Sciences | Mathematics

# Aims and Objectives

Mathematics is becoming more necessary in our technological world. Mathematical modeling and critical thinking can solve problems in business, ecology, science, government, and social sciences. Employers look for individuals who can think critically, solve problems, and write their results in a comprehensive and coherent fashion. The mathematics curriculum, the Ursuline Studies program, small classes that encourage questions and participation, and interdisciplinary studies that constitute the liberal arts core work together to this end.

Mathematics Fact Sheet

## Course Requirements

Major

The mathematics major requires 32 credit hours. Students are required to take 11 credit hours of MAT 221, 222, and 420, and choose 21 credit hours of electives to complete the 32 credits. These electives include MAT 223, MAT 310, MAT 311, MAT 312, MAT 324, MAT 212, MAT 412, MAT 313, MIS 260, PY 201, and PY 202.

Students desiring practical experience are encouraged to participate in the internship and/or cooperative education program. Students who are thinking of pursuing graduate work in mathematics are encouraged to speak to department faculty early in their academic careers to plan for any additional courses that would be beneficial to take, especially those that they might need to take at a neighboring college. Students are welcome to explore test-out opportunities to earn credits.

# Minor

Students seeking a minor in mathematics are required to take 128 credit hours. The 49 credit hours of the 128 credits are for the writing intensive core curriculum, the Ursuline Studies Program. The core curriculum includes mathematics, science, sociology, psychology, history, the arts, philosophy, and religious studies.

The 20 credit hours of the 128 are needed to fill the requirements for the mathematics minor. Students are required to take 8 credit hours of MAT 221 and 222, and choose 12 credit hours of mathematics electives to complete the 20 credits of mathematics courses. These electives include MAT 223, MAT 310, MAT 311, MAT 312, MAT 324, MAT 420, MAT 212, MAT 412, and MAT 313.

Students take other elective courses to complete the remaining 59 credit hours of the 128 credit hours required for their chosen major.

## Course Descriptions

MAT 099

Basic Mathematics (3)

A study of whole numbers, prime numbers, fractions, mixed numbers, decimal numbers, ratios and proportions, percent, introduction to algebra, measurement, and geometry. This course does not count toward degree requirements and is graded PA, PB, PC and D/NC or F/NC. Prerequisites: Placement.

MAT 114

Algebra (3)

A study of real numbers, algebraic expressions, linear equations and inequalities, straight lines and functions, exponents and polynomials, factoring polynomials and solving quadratic equations. Prerequisites: Completion of MAT 099 or equivalent with a passing grade, or placement.

MAT 125

Quantitative Reasoning (3)

A study of problem solving, numbers in the real world, financial management, statistical reasoning, probability, exponential astonishment, modeling with geometry and mathematics in the arts.

Ursuline Studies Stage I Math satellite.

Prerequisites: Completion of MAT 114 or equivalent with a grade of C or better, or placement.

MAT 131

College Algebra (4)

This course covers fundamentals of algebra, functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions of angles. Ursuline Studies Stage I Math satellite. Prerequisites: Completion of MAT 114 or equivalent with a grade of C or better, or placement.

MAT 132

Precalculus (4)

This course covers trigonometric functions of real numbers, analytic trigonometry, systems of equations and inequalities, topics in analytic geometry. Prerequisites: Completion of MAT 131 with a grade of C or better, or placement. Ursuline Studies Stage I Math satellite.

MAT 204

Teaching Middle School Math (3)

For students seeking license to teach mathematics in grades 4 to 9, this course reviews the content of the grade-specific competencies outlined by the Ohio Department of Education standards. Students are given opportunities to explore and practice teaching these topics, as well as make connections among different topics. The incorporation of visual aids and modern technology, in the form of calculators, spreadsheets, and Internet links, will be used to help bring these topics to life. Prerequisites: MAT 131

MAT 212

Statistics (3)

A study of elementary concepts and procedures basic to scientific, social, psychological and other areas; frequency distributions, normal distributions; measure of central tendency and dispersion; probability; samples and populations; correlation and regression; chi-square test; analysis of variance, hypothesis testing. A working knowledge of basic algebra is needed. Ursuline Studies Stage I Math satellite.

MAT 221

Calculus I (4)

This course covers functions, limits and rates of change, derivatives, application of differentiation, integrals, and applications of integration. Ursuline Studies Stage I Math satellite. Prerequisites: Completion of MAT 132 or equivalent with a grade of C or better, or placement.

MAT 222

Calculus II (4)

This course covers inverse functions, techniques of integration, further applications of integration, parametric equations and polar coordinates, and infinite sequences and series. Ursuline Studies

Stage I Math satellite.

Prerequisites: Completion of MAT 221 with a grade of C or better, or placement.

MAT 223

Calculus III (4)

This course covers vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, and vector calculus. Prerequisites: Completion of MAT 222 with a grade of C or better, or placement.

MAT 310

Number Theory (3)

An introduction to mathematical proof and mathematics beyond the beginning level, including a study of the divisibility properties of integers, prime numbers, linear and quadratic congruencies, and primitive roots. Prerequisites: MAT 221.

MAT 311

Abstract Algebra (3)

Fundamental concepts of abstract algebra, groups, rings, integral domains and fields.

MAT 312

Higher Geometries (3)

Development of postulation systems, critical study of Euclidean geometry as related to other geometries, including projective and hyperbolic.

MAT 313

Linear Algebra (3)

Vectors, real vector spaces, bases, linear transformations, matrix algebra, determinants, applications of matrices to linear programming; fields of business, economics, sociology, politics and biology.

MAT 324

Differential Equations (3)

Topics studied are the common types of differential equations and their applications. Prerequisite: MAT 222.

MAT 412

Advanced Statistics (3)

Topics studied are two- and three-factor analysis of variance, multifactor analysis of variance, various correlation coefficients, multiple regression, multiple comparisons and analysis of covariance. Prerequisite: MAT 212.

MAT 420

History of Mathematics (3)

Topics studied are the historical development of mathematics and integration of the various areas of mathematics with emphasis on the human endeavor. Prerequisites: MAT 221, 222, and one of the following: MAT 310, 311 or 312.

MAT 461, 462

Independent Study (credit varies)

Directed study of a special topic or area. Approval of department chair required.

MAT 475

Academic Internship (credit varies)

Opportunity for the student of mathematics to learn and work in an areas to which mathematics is applied, such as computers, statistics, business, or actuarial science.

MAT 288, 488

Special Topics (credit varies)

Math Alumnae Jessica Korkosz '09, MBA '13 from Ursuline College on Vimeo.

Mathematics Fact Sheet

Major

Students desiring practical experience are encouraged to participate in the internship and/or cooperative education program. Students who are thinking of pursuing graduate work in mathematics are encouraged to speak to department faculty early in their academic careers to plan for any additional courses that would be beneficial to take, especially those that they might need to take at a neighboring college. Students are welcome to explore test-out opportunities to earn credits.

The 20 credit hours of the 128 are needed to fill the requirements for the mathematics minor. Students are required to take 8 credit hours of MAT 221 and 222, and choose 12 credit hours of mathematics electives to complete the 20 credits of mathematics courses. These electives include MAT 223, MAT 310, MAT 311, MAT 312, MAT 324, MAT 420, MAT 212, MAT 412, and MAT 313.

Students take other elective courses to complete the remaining 59 credit hours of the 128 credit hours required for their chosen major.

MAT 099

Basic Mathematics (3)

A study of whole numbers, prime numbers, fractions, mixed numbers, decimal numbers, ratios and proportions, percent, introduction to algebra, measurement, and geometry. This course does not count toward degree requirements and is graded PA, PB, PC and D/NC or F/NC. Prerequisites: Placement.

MAT 114

Algebra (3)

A study of real numbers, algebraic expressions, linear equations and inequalities, straight lines and functions, exponents and polynomials, factoring polynomials and solving quadratic equations. Prerequisites: Completion of MAT 099 or equivalent with a passing grade, or placement.

MAT 125

Quantitative Reasoning (3)

A study of problem solving, numbers in the real world, financial management, statistical reasoning, probability, exponential astonishment, modeling with geometry and mathematics in the arts.

Ursuline Studies Stage I Math satellite.

Prerequisites: Completion of MAT 114 or equivalent with a grade of C or better, or placement.

MAT 131

College Algebra (4)

This course covers fundamentals of algebra, functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions of angles. Ursuline Studies Stage I Math satellite. Prerequisites: Completion of MAT 114 or equivalent with a grade of C or better, or placement.

MAT 132

Precalculus (4)

This course covers trigonometric functions of real numbers, analytic trigonometry, systems of equations and inequalities, topics in analytic geometry. Prerequisites: Completion of MAT 131 with a grade of C or better, or placement. Ursuline Studies Stage I Math satellite.

MAT 204

Teaching Middle School Math (3)

For students seeking license to teach mathematics in grades 4 to 9, this course reviews the content of the grade-specific competencies outlined by the Ohio Department of Education standards. Students are given opportunities to explore and practice teaching these topics, as well as make connections among different topics. The incorporation of visual aids and modern technology, in the form of calculators, spreadsheets, and Internet links, will be used to help bring these topics to life. Prerequisites: MAT 131

MAT 212

Statistics (3)

A study of elementary concepts and procedures basic to scientific, social, psychological and other areas; frequency distributions, normal distributions; measure of central tendency and dispersion; probability; samples and populations; correlation and regression; chi-square test; analysis of variance, hypothesis testing. A working knowledge of basic algebra is needed. Ursuline Studies Stage I Math satellite.

MAT 221

Calculus I (4)

This course covers functions, limits and rates of change, derivatives, application of differentiation, integrals, and applications of integration. Ursuline Studies Stage I Math satellite. Prerequisites: Completion of MAT 132 or equivalent with a grade of C or better, or placement.

MAT 222

Calculus II (4)

This course covers inverse functions, techniques of integration, further applications of integration, parametric equations and polar coordinates, and infinite sequences and series. Ursuline Studies

Stage I Math satellite.

Prerequisites: Completion of MAT 221 with a grade of C or better, or placement.

MAT 223

Calculus III (4)

This course covers vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, and vector calculus. Prerequisites: Completion of MAT 222 with a grade of C or better, or placement.

MAT 310

Number Theory (3)

An introduction to mathematical proof and mathematics beyond the beginning level, including a study of the divisibility properties of integers, prime numbers, linear and quadratic congruencies, and primitive roots. Prerequisites: MAT 221.

MAT 311

Abstract Algebra (3)

Fundamental concepts of abstract algebra, groups, rings, integral domains and fields.

MAT 312

Higher Geometries (3)

Development of postulation systems, critical study of Euclidean geometry as related to other geometries, including projective and hyperbolic.

MAT 313

Linear Algebra (3)

Vectors, real vector spaces, bases, linear transformations, matrix algebra, determinants, applications of matrices to linear programming; fields of business, economics, sociology, politics and biology.

MAT 324

Differential Equations (3)

Topics studied are the common types of differential equations and their applications. Prerequisite: MAT 222.

MAT 412

Advanced Statistics (3)

Topics studied are two- and three-factor analysis of variance, multifactor analysis of variance, various correlation coefficients, multiple regression, multiple comparisons and analysis of covariance. Prerequisite: MAT 212.

MAT 420

History of Mathematics (3)

Topics studied are the historical development of mathematics and integration of the various areas of mathematics with emphasis on the human endeavor. Prerequisites: MAT 221, 222, and one of the following: MAT 310, 311 or 312.

MAT 461, 462

Independent Study (credit varies)

Directed study of a special topic or area. Approval of department chair required.

MAT 475

Academic Internship (credit varies)

Opportunity for the student of mathematics to learn and work in an areas to which mathematics is applied, such as computers, statistics, business, or actuarial science.

MAT 288, 488

Special Topics (credit varies)