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.

### CSCI 1151 - Computer Programming I

An introduction to computers and computer programming. Emphasis will be placed on problem-solving with examples and exercises from social, natural, and mathematical sciences. Techniques of flowcharting and structured programming, development of algorithms, and types of computer hardware will also be discussed. Intended for students with no previous programming experience. Hours credit: 4. A student may not receive credit for this course after taking CSCI 1156 or its equivalent.

### CSCI 1156 - Computer Programming Ii

A continuation of Computer Science 1151. Emphasis on top-down programming using methods. Topics include user-defined classes and advanced data types, arrays, recursion, algorithms for sorting and searching, exception handling, advanced GUIs and graphics, and embedding Java applets into HTML documents. Hours credit: 4. Prerequisite: CSCI 1151 or the equivalent.

### CSCI 2251 - Algorithms & Data Structures

Structures for the representation of data are considered: vectors, lists, queues, trees, heaps, hash tables, maps, and graphs. This course presents the logic behind choosing a particular structure, and the associated algorithms for using each structure. Fundamental algorithms for solving problems, including sorting, searching and graph algorithms are developed. General design, analysis and the study of complexity are emphasized. Hours credit: 4. Prerequisite: CSCI 1156.

### CSCI 2290 - Independent Study

### CSCI 3336 - Operating Systems

Design and implementation of operating systems. Mutual exclusion, concurrency, deadlock, process scheduling, memory management, and files systems. Hours credit: 4. Prerequisite CSCI 1156. Alternate years.

### CSCI 3346 - Software Development

This course provides an in-depth study of steps in the software-development process: user requirements, specifications, design, implementation, testing, maintenance, documentation, and management. Students will develop the facility to apply the general principles to new problems. Hours credit: 4. Prerequisite CSCI 2251. Alternate years.

### CSCI 3386 - Csci One Time Only

Hours credit: 4. One-time only.

### CSCI 4492 - Professional Dev Sem

Students will explore how the skills they have accumulated over the course of their degree may be applied both to solve problems in the real world and to extend the limits of human knowledge. They will select a research advisor and a research topic in computer science and begin directed readings. Credit hours:1. Prerequisite: CSCI 251.

### DSCI 2232 - Intro To Data Science

Data science is an interdisciplinary field incorporating statistical techniques with algorithms to collect and to process large data sets, in order to extract meaning and make decisions. Students will explore the collection and filtering of data, machine learning algorithms, and methods for drawing conclusions. Credit hours: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395. Identical with MATH 2232.

### DSCI 2233 - Machine Learning

A broad introduction to machine learning and statistical pattern recognition. Unsupervised and supervised learning algorithms including dimensionality reduction (PCA and variants), clustering (simple clustering, agglomerative and non-agglomerative), probabilistic models, neural networks, and support vector machines. Hours: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395.

### DSCI 4495 - Data Science Seminar

The seminar requires students to explore the areas of their personal interest in data science in order to inform their choice of research topics, graduate school, and employment. Students will review the major ideas in data science and will prepare for the rigorous data science-related job interview. Hours: 1.

### MATH 1109 - 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: 4. Students considering Curricular Studies should not register for this course, as students may not receive credit for both MATH 1109 and MATH 2208

### MATH 1117 - Precal Elem Modeling I

Relations defined algebraically, graphically, and numerically. Functions, including polynomial, rational, trigonometric, exponential, and logarithmic. Applications, including modeling. Algebraic techniques, and a review of basic geometric relationships. Hours: 4. Not open to students who have been placed into MATH 1119 or above, except by permission of the Department.

### MATH 1118 - Precal Elem Modeling Ii

Relations defined algebraically, graphically, and numerically. Functions, including polynomial, rational, trigonometric, exponential, and logarithmic. Applications, including modeling. Algebraic techniques, and a review of basic geometric relationships. Hours: 4. Not open to students who have been placed into MATH 1119 or above, except by permission of the Department.

### MATH 1119 - Precalculus

A study of the properties of various functions, including polynomial, trigonometric, exponential, and logarithmic. Analytic geometry of conic sections. Hours credit: 4. Prerequisite: Mathematics 1113 or the equivalent. Not open to students who have been placed into Mathematics 1149 or above, except by permission of the Department.

### MATH 1149 - 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: 4. Prerequisite: Mathematics 1119R or the equivalent.

### MATH 1150 - Calculus Ii

A continuation of Mathematics 1149R. 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: 4. Prerequisite: Mathematics 1149R or permission of the Department.

### MATH 2227 - 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: 4. Not open to students who have satisfactorily completed Mathematics 3343. A student may receive credit for two of these courses: ECON 2227, MATH 2227, POL 2231, PSYC 2227 or SOC 3395. Offered second semester.

### MATH 2229 - 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 2232 - Introduction To Data Science

Data science is an interdisciplinary field incorporating statistical techniques with algorithms to collect and to process large data sets, in order to extract meaning and make decisions. Students will explore the collection and filtering of data, machine learning algorithms, and methods for drawing conclusions. Hours credit: 4. Prerequisite: ECON 2227 or EVST 2205 or MATH 2227 or MATH 3343 or POL 2231 or PSYC 2227 or SOC 3395. Alternate years.

### MATH 2234 - Techniques Of Mathematical Proof

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: 4. Prerequisite: Mathematics 1149R.

### MATH 2241 - Linear Algebra

Systems of linear equations, vector spaces and subspaces, bases and dimension, linear transformations, eigenvalues and eigenvectors, and inner product spaces. Hours credit: 4. Prerequisite: Mathematics 1149 or permission of the Department.

### MATH 2250 - 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: 4. Prerequisite: Mathematics 1150 and either MATH 2241 or PHYS 1115, or permission of the Department.

### MATH 2273 - Math One Time Only

Hours credit: 4. One time only.

### MATH 2286 - Math One Time Only

One time only.

### MATH 2286S - One Time Only Summer

One time only summer.

### MATH 3320 - 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: 4. Prerequisite: MATH 2241 or permission of the Department.

### MATH 3331 - 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: 4. Prerequisite: Mathematics 1150 and 2241, or the course may be taken concurrently with MATH 2241 by permission of the Department.

### MATH 3337 - 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: 4. Prerequisite: Mathematics 1150 or permission of the Department. Offered alternate years.

### MATH 3343 - 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: 4. Prerequisite: Mathematics 2250. Offered alternate years.

### MATH 3353 - 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: 4. Prerequisites: MATH 1150 and 241. Offered alternate years.

### MATH 3360 - Abstract Algebra

Groups, rings, integral domains. Homomorphisms and isomorphisms. Elementary properties of the integers. The fields of rational, real, and complex numbers. Hours credit: 4. Prerequisite: Mathematics 2241 or permission of the Department.

### MATH 3388 - Math One Time Only

Hours credit: 4. One time only.

### MATH 3390 - Independent Study

### MATH 4426 - 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: 4. Prerequisite: Mathematics 2250. Offered alternate years.

### MATH 4443 - Introduction To Analysis

A rigorous study of limits, continuity, differentiation, and integration of functions of a real variable. Hours credit: 4. Prerequisite: Mathematics 2250 or permission of the Department.

### MATH 4490 - Independent Study

### MATH 4492 - Professional Devel Sem

Students will explore how the skills they have accumulated over the course of their degree may be applied both to solve problems in the real world and to extend the limits of human knowledge. They will select a research advisor and a research topic in mathematics and begin directed readings. Credit hours:1. Prerequisite: MATH 360.

### MATH 4494 - Senior Seminar

This course will emphasize the importance of seminal problems in mathematics in motivating the development of techniques learned over the course of four years. Students will place their accumulated mathematical knowledge in context in the broad world of mathematics. Students will continue to conduct research into their broader world of mathematical knowledge. Students will continue to explore their chosen problem in mathematics or computer science, culminating in a paper and a talk on the topic. Credit hours: 4. Prerequisite: MATH 4493 or CSCI 4493.