# Mathematics

**Chaired by Patricia Garruto.**

The department offers a B.A. in Mathematics and a Minor in Mathematics.

Students are required to successfully complete the course MA 450 Coordinating Seminar. This course reviews the mathematics concepts that students learned in their major required courses and introduces new topics that are not covered in the major courses. In addition, this course is designed to assess the students’ understanding of important concepts and mathematical techniques in these courses, their ability to see the connectivity among the different areas of mathematics, and their ability to communicate mathematics in a clear and coherent manner. Students are given a set of essay questions to be researched in this course. These questions are broad in nature and deal with the underlying concepts that tie together the different areas in the major. An oral presentation of one of the questions is required. Results of the outcomes assessment are used by faculty to determine if content of the courses or the curriculum needs to be revised.

### Students who major in mathematics must complete:

**Short Title :** Appl.Stat.I

**Course Code :** MA 207

**Course Description :**

Introduces the fundamentals of statistics as employed in a variety of disciplines. Includes sampling, descriptive statistics, probability, discrete and continuous probability distributions, hypothesis testing, correlation and regression.

**Prerequisites :**

MA120, MA131, MA130, MA112, MA222, MA140, MA220, MA116, MA106, Core requirement in mathematics.

- Credit : 3

**Short Title :** Linear Algebra

**Course Code :** MA 214

**Course Description :**

Studies the properties and techniques of matrices, determinants, vector spaces, bases, linear dependence, linear transformation and orthogonality.

**Prerequisites :**

MA131

- Credit : 3

**Short Title :** Calculus I

**Course Code :** MA 220

**Course Description :**

Develops the basic theorems of calculus; develops the concepts of limit and continuity; studies techniques for finding the limit and the derivative of algebraic and trigonometric functions; applies the techniques of calculus to curve sketching, the study of motion and other fields of application; introduction to integral calculus.

**Prerequisites :**

MA131 or placement test

- Credit : 4 – 0

**Short Title :** Calculus II

**Course Code :** MA 221

**Course Description :**

Continues the development of the basic theorems of calculus; applications of the integral; differentiation and integration of exponential, logarithmic, trigonometric and inverse trigonometric functions; and some techniques of integration.

**Prerequisites :**

MA220 or placement test

- Credit : 4

**Short Title :** Modern Geometry

**Course Code :** MA 307

**Course Description :**

Considers the axiomatic approach to geometry; compares the various analyses of Euclid?s Fifth Postulate and resulting non-Euclidean geometries; studies several finite geometries.

**Prerequisites :**

MA309 or Departmental approval.

- Credit : 3

**Short Title :** Foundations Of

**Course Code :** MA 309

**Course Description :**

Introduction to concepts and tools used in abstract mathematics. Emphasis on writing of proofs. Elementary logic and set theory, formal axiom systems, transfinite numbers, the real number system, and the foundations of mathematics.

**Prerequisites :**

MA221, MA220

- Credit : 3

**Short Title :** Math-Tech Ii

**Course Code :** MA 413

**Course Description :**

This course provides a comprehensive hands-on introduction to the fundamental concepts of multimedia development. Topics include hypermedia development, development of an interactive learning tools, exploration of research issues related to hypermedia technology on the learning process, integration and synchronization of multimedia, including text, graphics, animation, digital video, and sound.

**Prerequisites :**

MA221

- Credit : 3

**Short Title :** Calculus III

**Course Code :** MA 324

**Course Description :**

Extends the study of the techniques of integration; studies series, parametric equations, conic sections and vectors in a plane; includes applications.

**Prerequisites :**

MA221

- Credit : 4

**Short Title :** Calculus IV

**Course Code :** MA 325

**Course Description :**

Completes the study of series and vectors and extends the concepts and techniques of the calculus of one variable to several variables.

**Prerequisites :**

MA214, MA324

- Credit : 3

**Short Title :** Abstract Algebr

**Course Code :** MA 420

**Course Description :**

Explores algebraic structures?groups, rings, fields and integral domains; also, Peano?s postulates and elementary number theory.

**Prerequisites :**

MA309

- Credit : 3

**Course Code :** MA 450

**Course Description :**

This course will review the mathematics concepts that students learned in their major required courses, show the interconnectivity between the various mathematics disciplines, and introduce new topics that are not covered in the major courses. Also, students will be guided in their research questions for their outcomes assessment. Limited to second semester juniors and seniors. Pass/Fail.

- Credit : 1

### Requirements for a Mathematics Major with a Double Major in Education

#### Requirements for a Mathematics Major with a Double Major in Education

Students who major in mathematics must meet the requirements for a mathematics major and all the requirements of the School of Education concerning admission, continuance, and completion of the program.

### Requirements for Elementary School with Subject Matter Specialization: Mathematics Grades 5-8 (Middle School Mathematics) Certification

#### Requirements for Elementary School with Subject Matter Specialization: Mathematics Grades 5-8 (Middle School Mathematics) Certification

Candidates for the Mathematics Middle School Certification are required to complete a minimum of 15 credits in mathematics.

**Courses offered at Caldwell University for certification are:**

**Short Title :** Math Lib Art

**Course Code :** MA 105

**Course Description :**

This course is designed for liberal arts, social science, humanities and communications majors. Introductory topics include: cryptology; numeration systems; history of mathematics; basic statistics; and sets. This course is not open to students majoring in elementary education, mathematics, business, biology, chemistry, computer information systems, medical technology and nursing.

**Prerequisites :**

MA 090 or placement test

- Credit : 3

**Short Title :** Math Social Sci

**Course Code :** MA 106

**Course Description :**

This course places special emphasis on applications to business, social sciences and related fields. Introductory topics are selected from some of the following: algebra; functions; graphing; interpretation of charts and graphs; data analysis; statistics; simple and compound interest; and consumer mathematics. This course is open to all students.

**Prerequisites :**

MA 090 or placement test

- Credit : 3

**Short Title :** College Algebra

**Course Code :** MA 113

**Course Description :**

This course is designed to be an intensive college algebra course to prepare some students who are majoring in STEM subject areas for the transition from MA 090 Basic Algebra or high school math, to higher level mathematics courses. It will cover algebraic concepts, graphing techniques and calculator use.

**Prerequisites :**

MA 090 or placement test

- Credit : 3

**Short Title :** Exp Of Math

**Course Code :** MA 116

**Course Description :**

Introduces problem solving skills in mathematics. Topics also include number systems and operations, estimations, geometry, measurements, symmetries, and tessellations. Graphing calculators and other technologies will be introduced in the application of the topics. Oral and written communication will be emphasized. Not open to students majoring in mathematics, biology, and medical technology.

**Prerequisites :**

MA 090 or placement test

- Credit : 3 – 0

**Short Title :** Math Perspectiv

**Course Code :** MA 117

**Course Description :**

Topics include algebra, functions, graphing, probability, data analysis, statistics, and proportional reasoning. Graphing calculators and other technologies will be introduced in the application of the topics. Oral and written communication will be emphasized. Not open to students majoring in mathematics, biology, and medical technology.

**Prerequisites :**

MA 090 or placement test

- Credit : 3

**Course Code :** MA 125

**Course Description :**

This course examines the nature of mathematics and provides an understanding of the role of mathematics in people's everyday lives and its extension into the global community. In addition to the study of mathematicians, the history of mathematics and numeration systems, students will explore mathematics as it relates to situations from any of the following areas such as architecture and construction, art, cryptography, fractals, music, nature, and sets. This course is open to all students and fulfills the Global Awareness and Cultural Understanding cluster in the enriched core.

**Prerequisites :**

none

- Credit : 3

**Short Title :** F. Analysis I

**Course Code :** MA 130

**Course Description :**

Studies the real number system, algebraic expressions, exponents, radicals, solutions of equations and inequalities, rational and polynomial functions; emphasizes the use of algebraic techniques in the solution of problems from a variety of disciplines.

**Prerequisites :**

MA 090 or placement test

- Credit : 3

**Short Title :** F. Analysis II

**Course Code :** MA 131

**Course Description :**

Concentrates on the exponential logarithmic trigonometric and inverse trigonometric functions, their graphs, properties and relations; also included are polar coordinates and the conic sections. Recommended as preparation in trigonometry for the study of calculus.

**Prerequisites :**

MA 130

- Credit : 3

**Short Title :** Appl.Stat.I

**Course Code :** MA 207

**Course Description :**

Introduces the fundamentals of statistics as employed in a variety of disciplines. Includes sampling, descriptive statistics, probability, discrete and continuous probability distributions, hypothesis testing, correlation and regression.

**Prerequisites :**

MA120, MA131, MA130, MA112, MA222, MA140, MA220, MA116, MA106, Core requirement in mathematics.

- Credit : 3

**Short Title :** Linear Algebra

**Course Code :** MA 214

**Course Description :**

Studies the properties and techniques of matrices, determinants, vector spaces, bases, linear dependence, linear transformation and orthogonality.

**Prerequisites :**

MA131

- Credit : 3

**Short Title :** Linear Alg II

**Course Code :** MA 216

**Course Description :**

Extends the study of Linear Algebra. Topics include eigenvalues and eigenvectors, LU-facotrization, the application of systems of linear equations, matrix operations, determinants, vector spaces, inner product spaces, and linear transformations.

**Prerequisites :**

MA221, MA214

- Credit : 3

**Short Title :** History Of Math

**Course Code :** MA 218

**Course Description :**

This course eplores a variety of themes in mathematics, such as, calculation, number bases, geometry, algebra, infinity and analytic geometry. Studies will include historical development and contributions for various civiliziations ranging from Babylonia and Egypt and the Middle East and onto modern Europe. In addition, to gaining, a deeper understanding of mathematics, students will pbtain an appreciation of the role mathematics has played for centuries in a variety of cultures.

**Prerequisites :**

MA112, MA118, MA220 Calculus I

- Credit : 3

**Short Title :** Calculus I

**Course Code :** MA 220

**Course Description :**

Develops the basic theorems of calculus; develops the concepts of limit and continuity; studies techniques for finding the limit and the derivative of algebraic and trigonometric functions; applies the techniques of calculus to curve sketching, the study of motion and other fields of application; introduction to integral calculus.

**Prerequisites :**

MA131 or placement test

- Credit : 4 – 0

### Actuarial Science Concentration (35 Credits)

**Background and Rationale:**

Actuarial Science is an area of study that analyzes and assesses the financial impact of risk. There exists a need to forecast financial risk to improve decision-making in many businesses and government agencies. To successfully address this growing field, the Mathematics Department and the School of Business have designed an in

**Mathematics (17 Credits)**

**Short Title :** Calculus I

**Course Code :** MA 220

**Course Description :**

Develops the basic theorems of calculus; develops the concepts of limit and continuity; studies techniques for finding the limit and the derivative of algebraic and trigonometric functions; applies the techniques of calculus to curve sketching, the study of motion and other fields of application; introduction to integral calculus.

**Prerequisites :**

MA131 or placement test

- Credit : 4 – 0

**Short Title :** Calculus II

**Course Code :** MA 221

**Course Description :**

Continues the development of the basic theorems of calculus; applications of the integral; differentiation and integration of exponential, logarithmic, trigonometric and inverse trigonometric functions; and some techniques of integration.

**Prerequisites :**

MA220 or placement test

- Credit : 4

**Short Title :** Linear Algebra

**Course Code :** MA 214

**Course Description :**

Studies the properties and techniques of matrices, determinants, vector spaces, bases, linear dependence, linear transformation and orthogonality.

**Prerequisites :**

MA131

- Credit : 3

**Short Title :** Prob & Stat I

**Course Code :** MA 311

**Course Description :**

An introduction to the theory of probability and statistics utilizing methods from calculus. Topics include the axioms and rules of probability, Bayes? Theorem, discrete and continuous random variables, univariate probability distributions, expectation, variance, and generating functions.

**Prerequisites :**

MA221

- Credit : 3

**Short Title :** Prob & Stat II

**Course Code :** MA 312

**Course Description :**

Extends the study of the theory of probability and statistics. Topics include multivariate probability distributions, Central Limit Theorem, covariance, correlation, point estimation, and hypothesis testing.

**Prerequisites :**

MA311

- Credit : 3

#### BUSINESS (18 CREDITS)

**Business (18 Credits)**

**Course Code :** BU 211

**Course Description :**

This course introduces fundamental principles in financial accounting. It provides a basic understanding of accounting theory, practices, and procedures through the accounting cycle as well as recording transactions in journals and ledgers. The course introduces the basic financial statements of balance sheet, income statement, and statement of owner's equity, explaining their purpose and composition.

**Prerequisites :**

MA131, MA140, MA220, MA106, MA130, MA221, MA112 or other equivalent math core with grade of B- or higher.

- Credit : 3

**Short Title :** Accounting II

**Course Code :** BU 212

**Course Description :**

This course covers the measurement and reporting of claims by creditors and equity investors; explains business structures of partnerships and corporations; and covers topics such as income taxes and financial analysis. The course introduces the statement of cash flows, its purpose and composition.

**Prerequisites :**

BU211

- Credit : 3

**Short Title :** Principles of Economics I

**Course Code :** BU 205

**Course Description :**

This course introduces students to the fundamentals of microeconomic theory. It deals with the behavior of individual economic units that are small relative to the national economy. The course explains how consumers, workers, investors, owners of land, and business firms make their decisions, and how they interact to form larger units of markets and industries. A thorough survey of market failure and government failure also will be covered.

**Prerequisites :**

MA 112 or other equivalent math core with grade of B- or higher

- Credit : 3

**Short Title :** Principles of Economics II

**Course Code :** BU 210

**Course Description :**

This course introduces students to the fundamentals of macroeconomic theory. It deals with aggregate economic quantities, such as the level and growth rate of national output, interest rates, unemployment, and inflation. The course explains how the aggregate markets for goods and services, for labor, and for corporate stocks and bonds are formed, what the trade-off is between inflation and unemployment, and how the government develops and implements its monetary and fiscal policies.

**Prerequisites :**

BU205

- Credit : 3

**Short Title :** Finance

**Course Code :** BU 337

**Course Description :**

Introduces the techniques employed by firms in raising and allocating funds. Describes analytical tools used by financial managers.

**Prerequisites :**

BU305, BU210, BU212, MA311, MA207

- Credit : 3

**Short Title :** Business Spreadsheet Applications

**Course Code :** CS 219

**Course Description :**

This course emphasizes analysis and solutions to contemporary business problems through the use of the current version of Microsoft Excel. Students are introduced to business decision modeling processes to strengthen logical reasoning and analytical skills. Microsoft Excel is used as the basis for managerial decision support through analysis of contemporary business case problems. Students apply the appropriate functions and features of Microsoft Excel to solve business cases. The course also emphasizes oral presentation and written reports on business processes used in case solutions to further strengthen students’ communication skills.

**Prerequisites :**

CS115, CS115X, MA207, MA112

- Credit : 3

### Your degree includes credits from Liberal Arts and Sciences Core, Major, and Electives.

### Core Requirement

The choice of course to meet the core requirement in mathematics depends on: a) results of a college-administered mathematics placement test; b) secondary school preparation; and c) potential major. Students are assigned to a developmental course, a 100-level course or a 200-level course.

# A Catholic Liberal Arts Education

At the core of a Caldwell education is our liberal arts curriculum, designed to guide students to critical thinking skills, appreciate diverse cultures, and acquire a moral and civic awareness.

Students develop the whole self as they absorb learning through our liberal arts core: the humanities; the physical and biological sciences, and mathematics; and the social sciences.