John Ong, department head

Sara Botkin, Kari Frenz, Joseph Johnson, Christy Lowery-Carter, Mike Riddell

The mathematics curriculum at Mary Baldwin emphasizes the development of a student’s ability to think and engage in the process of problem solving. Techniques associated with logic, analysis, data manipulation, computing, pedagogy, and the understanding of mathematical assumptions and structures are taught. Students will be exposed to both pure and applied mathematics, gaining analytical and practical skills necessary for succeeding in industry, as an educator, or in graduate school.

**Requirements for the Bachelor of Arts in Mathematics**

35 semester hours

MATH 211

MATH 212

MATH 231

MATH 301

MATH 302

MATH 306

MATH 322

MATH 398

MATH 401

And additional courses in Math numbered above 200 to total 35 s.h. Note that a maximum of 3 sh of Math 380: Teaching Assistantship may count toward the mathematics major.

**Requirements for the Bachelor of Science in Mathematics**

50 semester hours

All of the requirements listed for the BA, plus the following:

PHYS 201

PHYS 202

One of MATH 233, 234, 304, or 398 not counted in the BA.

One other 200-level laboratory science course.

**Requirements for the Minor in Mathematics**

20 semester hours

MATH 211

MATH 212

MATH 231

And additional courses in Math numbered above 200 to total 20 s.h. Math 380 may not count toward the minor.

**Program in Applied Mathematics**

*Please see **Mathematics — Applied*

**Recommended Programs**

**For teachers of mathematics:
**Students at Mary Baldwin University may obtain a BA in Mathematics with a Math Education Emphasis, or elect to participate in a 4-1 program leading to the BA and a Master of Arts in Teaching (MAT) degree. Interested students should contact Dr. Ong or Dr. Johnson in the mathematics department in their first semester at college. Students in this program are encouraged to apply to be math tutors and to sign up for a teaching assistantship in mathematics.

**Requirements for the Bachelor of Arts in Mathematics with Math Education Emphasis**

41 semester hours

MATH/ED 156

MATH/ED 158

MATH 211

MATH 212

MATH 221

MATH 231

MATH 233

MATH 301

MATH 322

MATH 398

MATH 401 or ED 400

ED 602 or ED 115

ED 622 or ED 120, or IN 601

**Additional requirements**:

Besides the above courses, the student must complete a minor in Education with a mathematics placement in their practicum ED 110. The committee formed for evaluating the student’s senior project will include at least one faculty member from each discipline of both mathematics and education.

**For graduate study in mathematics:
**MATH 211, MATH 212, MATH 221, MATH 231, MATH 233, MATH 301, MATH 302, MATH 304, MATH 306, MATH 311, MATH 322, MATH 370, MATH 398 in both the junior and senior year, MATH 401. Directed inquiry courses in Topology and Complex Analysis are strongly recommended. Students in this program should also apply to be math tutors at the College.

**For graduate study in statistics:
**MATH 211, MATH 212, MATH 231, MATH 233, MATH 234, MATH 301, MATH 302, MATH 304, MATH 306, MATH 311, MATH 322, MATH 370, MATH 398, MATH 401. Students are encouraged to take statistics courses offered by other disciplines.

**Mathematics Course Descriptions **

**155 Mathematics in Contemporary Society** (3 s.h.) (**Q**)

Students will investigate mathematical topics in relationship to life in contemporary society. The course will emphasize quantitative reasoning in the context of applications, focusing on mathematical modeling and critical analysis of real-world problems. Topics to be covered may include basic probability and statistics, mathematical modeling, finance, voting and appointment, and logic. Supplemental topics may be introduced depending on the interests of students enrolled in the course.

**156 Numeration and Algebra for Teachers** (3 s.h.) (**Q**)

The course reviews content of the numeration, computation & estimation, and algebra strands of the Virginia SOL for grades K-6 from a teacher and student perspective. Students develop deeper understanding of content, flexibility in solving problems, and an ability to work with a variety of algorithms and manipulatives that are appropriate for this grade span. Representing abstract mathematical concepts in developmentally appropriate ways is emphasized. Emphasis will be on exploration, problem solving, appropriate technology usage, and designing tasks to develop deeper understanding of content as a student and future teacher. In addition, the course emphasizes the development of teaching styles with a focus on inquiry teaching and learning for the concepts. Students will design tasks that foster deeper understandings as they explore the concepts. Cross listed as ED 156.

**158 Geometry and Measurement for Teachers** (3 s.h.) (**Q**)

The course reviews concepts of geometry and measurement in the K-8 curriculum from a teacher and student perspective, with particular attention to Euclidean geometry, axiomatics, and deductive reasoning. Emphasis will be on exploration, inductive and deductive reasoning, problem solving, appropriate technology usage, and designing tasks to develop deeper understanding of content as a student and future teacher. Statistics will be addressed conceptually. In addition, the course emphasizes the development of teaching styles with a focus on inquiry teaching and learning for the concepts. Students will design tasks that foster a deep understanding of geometry and statistics as they explore the concepts. Cross listed as ED 158.

**159 College Algebra **(3 s.h.) (**Q**)

Students are provided with a background in algebra appropriate for the application of mathematics to other disciplines and for further study in mathematics. Topics include equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and systems of equations. Emphasis is on logical analysis, deductive reasoning, problem solving and modeling. **Prerequisite: MSAT 510 or MACT 20, or C- or higher in a Q course. *Fall and Spring semester.

**171 Precalculus with Trigonometry **(3 s.h.) (**Q**)

Algebraic, trigonometric, logarithmic and exponential functions are explored. The main emphasis will be on developing trigonometric functions and their properties, since they play an indispensable role in the modeling of physical phenomena and in the study of calculus. Included is a MAPLE software project on modeling and problem solving. **Prerequisite: MATH 159, or equivalent*. Fall and Spring semester.

**211, 212 Introduction to Calculus and Analytic Geometry I, II **(4 s.h. each) (**Q**)

MATH 211 is required for mathematics majors and recommended for majors in the sciences and economics. We treat the basic concepts of differential calculus and its applications, including limits, continuity, differentiation, the chain rule, the mean-value theorem, optimization problems, antiderivatives, and the fundamental theorem of calculus. Transcendental functions are covered. **Prerequisite: MATH 171*. Fall semester.

MATH 212 develops the concept of the definite integral and its applications. Integration of transcendental functions, integration techniques, L’Hopital’s Rule, and improper integrals are covered. We complete the course with infinite series and the Taylor Polynomials.**Prerequisite: MATH 211*. Spring semester.

**221 History of Mathematics **(3 s.h.) (**Q**)

This course will examine the development of mathematics using a blend of chronological and thematic approaches. Major topics include the conceptual and axiomatic development of numeracy, geometry, algebra, and calculus, with particular focus on Euclidean and non-Euclidean geometries, and the development of mathematical reasoning and proof throughout history. Students will explore the contributions of significant individuals in the history of mathematics, and will investigate contemporary mathematical topics as they relate to the major themes of the course.

**Prerequisite: MATH 211 or permission of instructor*. Alternate years.

**231 Discrete Mathematical Structures **(3 s.h.) (**Q**)

This is an introduction to techniques of theoretical mathematics. We will explore logic, truth tables, deductive proof and the principle of mathematical induction. Algorithms, algebraic structures, discrete probability, counting methods, relations, and graph theory are also covered. Some of the topics have substantial application to computer science. **Prerequisite: MATH 211*. Fall semester.

**233 Statistical Methods and Theory I** (3 s.h.) (**Q**)

An introduction to applied statistics and theory. Topics include measures of central tendency, discrete and continuous random variables, Normal distributions, Binomial distributions, sampling distributions and the Central Limit Theorem, probability, correlation and regression, producing data from sampling and experiments, hypothesis testing using the z, t, chi-square, and F distributions, confidence intervals, and analysis of variance. The statistical software package SPSS will be used to illustrate the material presented. **Prerequisite: B or higher in INT 222 and MATH 159, PSYC 250, or MATH 211*. Spring semester.

**234 Statistical Methods and Theory II** (3 s.h.) (**Q**)

This is a second course in applied statistics and theory. Topics include analysis of variance, multiple linear regression, and nonparametric statistical methods. The statistical software package SPSS will be used to illustrate the material presented. **Prerequisite:* *MATH 233*. Offered as needed.

**301 Multivariable Calculus I **(3 s.h.) (**Q**)

Math 301 covers the first semester of Multivariable Calculus. Subjects include: vectors, the dot and cross product, functions of several variable, partial derivatives, chain rule in multiple variables, directional derivatives and the gradient, and Lagrange multipliers. Next integration in two and three dimensions including polar integrals will be covered. Time permitting, cylindrical and spherical coordinates will complete the course.**Prerequisites: MATH 212*. Fall semester.

**302 Multivariable Calculus II **(3 s.h.) (**Q**)

Math 302 is the second semester of Multivariable Calculus. Subjects include: continuation of multiple integrals from the first semester, the calculus of vector valued functions, vector fields, integration over vector fields, The Fundamental Theorem for Line Integrals, Green’s Theorem, Stoke’s Theorem, and Gauss’s Theorem. Time permitting, proof techniques in advance calculus will be introduced.**Prerequisite: MATH 301*. Spring semester.

**304 Numerical Analysis and Computing **(3 s.h.) (**Q**)

This course surveys the techniques and algorithms of numerical computing, numerical solution of algebraic equations and differential equations, interpolation, approximation, and iteration theory, numerical differentiation and numerical integration, error analysis, stability and convergence of solutions. The computer algebra system *Maple *is used. **Prerequisite: MATH 301*. Alternate years.

**306 Ordinary Differential Equations **(3 s.h.) (**Q**)

This is the study of the theory and methods of initial value problems of first and second order equations as well as systems of first order linear equations with constant coefficients. Methods such as integrating factors, undetermined coefficients, variation of parameters and the linearization of nonlinear problems will be covered. Uniqueness and existence questions will be discussed. Differential equations is a powerful modeling tool and can be applied to diverse areas of study including environmental and population studies, radioactive decay, fluid flow, epidemiology and much of engineering. Students will be required to make a presentation in their area of interest. **Prerequisite: MATH 212, or MATH 306 may be taken concurrently with MATH 212 if you have a B in MATH 211*. Alternate years.

**311 Probability and Distribution Theory **(3 s.h.) (**Q**)

Sample-point and event-composition methods for calculating the probability of an event; Bayes’ rule; the binomial, geometric, hypergeometric and Poisson probability distributions; mathematical expectations; moment-generating functions; Tchebysheff’s theorem; continuous random variables and their probability distributions; multivariate probability distributions; and functions of random variables. This course is recommended for students planning to work in industry. **Prerequisites: 212*. Offered as needed.

**322 Linear Algebra **(3 s.h.) (**Q**)

This class develops the theory of vector spaces and its underlying relevance to matrices and systems of linear equations. Topics include the vector space Rn, abstract vector spaces, elementary operations and systems of linear equations, linear transformations, and eigenvectors and eigenvalues. Emphasis is on providing a bridge from the intuitive developments of lower level courses to the more rigorous abstract courses in mathematics. All students will be required to make a presentation on an application area. **Prerequisites: MATH 211 and 231*. Alternate years.

**370 Colloquium in Mathematics **(3 s.h.) (**Q**)

Selected topics in higher-level mathematics are offered which are not among our regular courses. The list below reflects the knowledge and expertise of the current faculty and are typical courses in an undergraduate curriculum. The colloquium is also used to introduce students to potential research areas. Topics include: Abstract Algebra II, Real Analysis II, Topology, Representation Theory, Introduction to Homotopy Theory, Fourier Analysis, Complex Analysis, Mathematical Modeling, Partial Differential Equations, Women in Mathematics, Mathematics Pedagogy, Introduction to Functional Analysis, Partially Ordered Groups, Graph Theory, Problem Solving Seminar, and Engineering Mathematics. Alternate years or through directed inquiry.

**398 Abstract Algebra I **or** Real Analysis I **(3 s.h. each) (**Q**)

MATH 398 alternates between abstract algebra one year and real analysis the next. Both courses develop mathematical maturity through the use of intuition, deductive logic and mathematical analysis. Abstract algebra studies the structures of axiomatic mathematical systems such as groups, rings and fields. Real analysis develops the mathematical techniques necessary to understand the real line as well as functions on the reals. MATH 398 may be repeated for credit and all students who plan to attend graduate school in Mathematics must take both courses. **Prerequisites: MATH 302, and MATH 322 or permission of instructor*. Fall semester.

**401 Senior Seminar **(3 s.h.) (**M**)

MATH 401 provides the structure under which students complete their senior research projects. Students must sign up for 1 s.h. of Senior Seminar in the fall and 2 s.h. of Senior Seminar in the spring of their senior year. Each student completes a faculty-approved research project, writes a senior paper based on the results, and presents the results to the mathematics faculty. The student is required to write a paper and pass an oral examination on the theory related to her research area, as well as propose her research project in the fall. She will perform her research in the spring semester, and defend her senior research project paper when done. This requirement applies to Adult Degree Program students as well. **Prerequisite: MATH 398* *or taken concurrently.*

**Note: **Directed inquiries, teaching assistantships, and internships are arranged on an individual basis. Internships and teaching assistantships may include service-oriented work in the community for fulfilling civic engagement requirements.