Randolph College > Academic Programs > Mathematics > Curriculum

## Mathematics Curriculum

The Department of Mathematics wishes to share the beauty and usefulness

of mathematics and computer science with as many undergraduates as possible; to provide training in analytical thinking; to prepare majors for advanced work in mathematics, computer science, and related fields; and to provide the background for various kinds of employment after graduation.

The faculty adheres to the philosophy that the only way to learn mathematics is to do it. Regular written assignments enable the student and faculty to monitor the student’s progress and to verify the accuracy of the substance and style of the work.

The Department’s emphasis is on strengthening the student’s problem-solving skills.

## Computer Science Minor

The study of computer science offers students the opportunity to develop problem solving facility and helps develop skills which have broad utility in theory and application and are amongst the most sought-after by employers. The abstraction of real-world problems, the construction of algorithms to display and transform data, and the theory of computation are all central concerns of computer science. The minor in computer science can be effectively combined with any major.

Whether studied with professional goals in mind, to supplement the study of any other field, or just for interest’s sake, computer science offers a powerful way to approach many challenging problems. When combined with selected courses in mathematics and physics, the minor will help prepare the student for graduate work in computer science and related fields.

## Independent Study for Non-Majors

The Department is pleased to offer independent study courses for one semester hour each on the application of mathematics to such fields as economics and business, political science, psychology, biology, chemistry, cryptology, linguistics, and physics. These courses are intended primarily for students in other disciplines who have done well in mathematics but do not wish to take additional three-hour mathematics courses.

Interested students should contact the Department.

## Course Offerings

Below is a list of available courses offered by the mathematics department. Consult the Registrar’s Office and the College Catalog for registration information.

### MATH 109 - INTRO TO QUANTITATIVE REASONING

This course presents mathematical ideas in a real world context. Topics covered include critical thinking and problem solving, the mathematics of finance, basic statistical principles, mathematics and the arts, and the theory of voting. Hours credit: 3. Students considering Curricular Studies should not register for this course, as students may not receive credit for both MATH 109 and MATH 208

### MATH 113 - ELEMENTARY MATHEMATICAL MODELING

This course explores mathematical models of natural phenomena such as population growth and radioactive decay. Analysis of data using computer technology. Linear, quadratic, general polynomial, exponential, and logarithmic models will be discussed. Hours credit: 3. Not open to students who have completed Mathematics 119R or above, except by departmental recommendation.

### MATH 119 - PRECALCULUS

A study of the properties of various functions, including polynomial, trigonometric, exponential, and logarithmic. Analytic geometry of conic sections. Hours credit: 3. Prerequisite: Mathematics 113 or the equivalent. Not open to students who have been placed into Mathematics 149 or above, except by permission of the Department.

### MATH 149 - CALCULUS I

Limits, continuity, and differentiation of algebraic functions of one variable. Applications to curve sketching, optimization, and rates of change. The definite integral applied to finding the area under a curve. Hours credit: 3. Prerequisite: Mathematics 119R or the equivalent.

### MATH 150 - CALCULUS II

A continuation of Mathematics 149R. Volumes and surface area of solids of revolution. Lengths of curves. The logarithm and exponential functions. Techniques of integration. Areas in polar coordinates. Improper integrals, infinite series, and power series. Hours credit: 3. Prerequisite: Mathematics 149R or permission of the Department.

### MATH 208 - CONCEPTS OF ELEM & MID SCHOOL MATHEMATIC

Introduces elementary problem solving with emphasis on the nature of numbers and the structure of the real number system. Topics studied include the structure and properties of number systems and of Euclidean Geometry applicable in elementary and middle school classrooms. This course is open to all students and required of students seeking elementary education licensure. Hours credit: 3.

### MATH 227 - ELEMENTARY APPLIED STATISTICS

An introduction to statistics, including probability, binomial distributions, normal distributions, sampling theory, testing hypotheses, chi-square tests, and linear regression. Hours credit: 3. Not open to students who have satisfactorily completed Mathematics 343. A student may receive credit for two of these courses: MATH 227, POL 231, PSYC 227R or SOC 395. Offered second semester.

### MATH 229 - ADVANCED MATHEMATICAL PROBLEM SOLVING

In this course, students will be expected to solve and present solutions to a collection of problems gathered from various mathematics competitions. Problem solutions may involve the techniques of classical algebra, geometry, calculus, and combinatorics. Hours credit: 1. Prerequisite: Permission of the Instructor. May be repeated for credit up to a maximum of 4 hours.

### MATH 234 - DISCRETE & COMBINATORIAL MATHEMATICS

An introduction to set theory and counting principles. Techniques of mathematical proof. Combinatorics, including recursion and generating functions. The theory and applications of graphs. Hours credit: 3. Prerequisite: Mathematics 149R.

### MATH 241 - LINEAR ALGEBRA

Systems of linear equations, vector spaces and subspaces, bases and dimension, linear transformations, eigenvalues and eigenvectors, and inner product spaces. Hours credit: 3. Prerequisite: Mathematics 149R or permission of the Department.

### MATH 250 - CALCULUS III

An introduction to vector calculus. Differential and integral calculus of more than one variable. Vector fields, including Green's, Stokes', and the Divergence Theorems. Hours credit: 3. Prerequisite: Mathematics 150R and either MATH 241 or PHYS 115, or permission of the Department.

### MATH 320 - INTRODUCTORY TOPOLOGY

An introduction to point-set geometry, including topological spaces, metric spaces, homotopy, the Urysohn lemma, and Tychonoff’s theorem. Students explore topology as the underpinning of modern geometry. Hours credit: 3. Prerequisite: MATH 241 or permission of the Department.

### MATH 331 - DIFFERENTIAL EQUATIONS

First order linear and non-linear equations, second and higher order linear equations, series solutions, Laplace transforms, and systems of linear differential equations. Applications, primarily to mechanics and population dynamics. Hours credit: 3. Prerequisite: Mathematics 150R and 241, or the course may be taken concurrently with MATH 241 by permission of the Department.

### MATH 337 - NUMBER THEORY

Properties of the integers. Unique factorizations, congruences and modular arithmetic. Diophantine equations, prime numbers, quadratic reciprocity, and integer functions. Applications to cyptology. Hours credit: 3. Prerequisite: Mathematics 150R or permission of the Department. Offered alternate years.

### MATH 343 - MATHEMATICAL STATISTICS

Probability. Discrete and continuous probability distributions. Sampling and the Central Limit Theorem. Confidence intervals, hypothesis testing, linear regression, and non-parametric tests. Hours credit: 3. Prerequisite: Mathematics 250. Offered alternate years.

### MATH 353 - MATHEMATICAL MODELING

The construction and analysis of mathematical models to solve problems in the physical and social sciences. Dynamical systems are emphasized with a particular concentration on linear and non-linear discrete dynamical systems. Topics may include dimensional analysis, stability, chaos, and fractals. Hours credit: 3. Prerequisites: MATH 150R and 241. Offered alternate years.

### MATH 360 - ABSTRACT ALGEBRA

Groups, rings, integral domains. Homomorphisms and isomorphisms. Elementary properties of the integers. The fields of rational, real, and complex numbers. Hours credit: 3. Prerequisite: Mathematics 241 or permission of the Department.

### MATH 390 - INDEPENDENT STUDY

### MATH 420 - NUMERICAL ANALYSIS

A study of algorithms for solving mathematical problems using computers. These problems include finding the roots of functions, solving systems of linear equations, interpolation, approximate integration, and solving differential equations. Implementation of these algorithms on the computer will be an important part of the course. Hours credit: 3. Prerequisite: MATH 150R and 241. Prerequisite or corequisite: CSCI 156. Offered alternate years.

### MATH 426 - COMPLEX VARIABLES

The complex number system. Limits, continuity, and differentiability of functions of a single complex variable. Contour integration and Cauchy's Theorem. The calculus of residues. Conformal mapping. Hours credit: 3. Prerequisite: Mathematics 250. Offered alternate years.

### MATH 443 - INTRODUCTION TO ANALYSIS

A rigorous study of limits, continuity, differentiation, and integration of functions of a real variable. Hours credit: 3. Prerequisite: Mathematics 250 or permission of the Department.

### MATH 494 - SENIOR SEMINAR

Readings on the history of mathematics from the seventeenth century through modern times. Oral reports by students and faculty on topics of interest in mathematics. Written reports are also required. Hours credit: 3. Prerequisite: Mathematics 360 and 443.