# Mathematics Minor Requirements

Department Chairperson:Hsin-hao Su

Phone: 508-565-1242
hsu@stonehill.edu

The minor in Mathematics requires the completion of eight courses.

## Complete Five Required Courses

Code Course Credits

### Calculus I

Offered: Fall and Spring Semesters

Calculus of a single variable: functions, limits, derivatives, differentiation rules, applications of derivatives, integrals, techniques of integration, applications of integration, infinite sequences and series, first and second order differential equations. May not receive credit for both MTH 125 and MTH 119.

4

### Calculus II

Offered: Fall and Spring Semesters

Calculus of a single variable: functions, limits, derivatives, differentiation rules, applications of derivatives, integrals, techniques of integration, applications of integration, infinite sequences and series, first and second order differential equations.

4

### Linear Algebra

Offered: Spring Semester

The development of the methods and underlying ideas for solving systems of linear equations. Topics include: vectors, matrices, linear transformations, determinants and eigenvectors. Use of mathematical software MAPLE, in applications.

4

### Multivariable Calculus

Offered: Fall Semester

Continuation of the sequence begun in Calculus I and II. Functions of several variables, analytic geometry, vectors, partial derivatives, multiple integration.

4

### Discrete Mathematics

Offered: Spring Semester

Sets operations, Countability, Functions, Number Theory, Equivalence Relations, Recurrence Relations, Graphs, Combinatorics, Probability.

3

## Complete Three 300 or 400-Level Mathematics Courses

Elective courses should be selected in consultation with a member of the mathematics faculty.

Code Course Credits

### Abstract Algebra I

Offered: Fall Semester

Groups, rings, fields, rings of polynomials, extension fields, automorphisms of fields, splitting fields, Galois theory.

3

### Abstract Algebra II

Offered: Spring Semester

Groups, rings, fields, rings of polynomials, extension fields, automorphisms of fields, splitting fields, Galois theory.

3

### Real Analysis I

Offered: Fall Semester

Rigorous development of the theory of calculus of one variable. Topics include: properties of the real line, sequences, series, limits, continuity and uniform continuity. Additional topics from differential and integral calculus of one or more variables.

3

### Real Analysis II

Offered: Spring Semester

Rigorous development of the theory of calculus of one variable. Topics include: properties of the real line, sequences, series, limits, continuity and uniform continuity. Additional topics from differential and integral calculus of one or more variables.

3

### Modern Geometry

Offered: Fall Semester

The axiomatic approach of Hilbert to Euclid’s Elements. Geometry from the viewpoint of rigid transformations. Non-Euclidean Geometry. The roles of coordinates, both global and local. Geometrizations of low dimensional manifolds.

3

### Differential Equations and Dynamics

Offered: Alternate Years: Spring 2016, 2018

An introduction to qualitative and quantitative methods for ordinary differential equations. Topics include first and second order equations, existence and uniqueness of solutions, logistic models, planar linear systems (including phase portraits), regular singular points. Other topics selected from: flows, the stable manifold theorem, and Laplace transforms.

3

### Combinatorics and Graph Theory

Offered: Alternate Years: Fall 2015, 2017

Methods for determining, given some well-defined operation, the number of ways it can be performed. Networks of dots and lines.

3

### Number Theory

Offered: Alternate Years: Spring 2017, 2019

Mathematical induction, prime numbers, Diophantine equations, congruences, sums of squares.

3

### Theory of Computation

Offered: Alternate Years: Fall 2016, 2018

For description and semester schedule see CSC 384.

3
CSC 384 - Theory of Computation

### Numerical Analysis

Offered: Alternate Years: Spring 2016, 2018

Both theoretical and practical problems in the computational aspects of mathematics: approximation of functions, numerical differentiation, solutions to algebraic and differential equations; topics in linear algebra.

3
CSC 393 - Numerical Analysis

### Probability and Statistics I

Offered: Alternate Years: Fall 2016, 2018

Mathematical theory of probability, axioms and basic properties, random variables; continuous and discrete distributions, moments, generating functions, special distributions, law of large numbers, central limit theorem. Use of mathematical software in applications.

3

### Probability and Statistics II

Offered: Alternate Years: Spring 2017, 2019

Continuation of MTH 395. Theory and application of statistics; random sampling; organization of data; descriptive statistics; sample mean and additional special distributions, the theory of estimators, applications of estimation, hypothesis testing and Regression. Mathematical software is used in applications of statistics.

3

### Topics in Mathematics

Offered: Not Offered 2015-2016

3

### Internship in Mathematics

Offered: Fall and Spring Semesters

Requires approval of the Department Chairperson.

Must complete the "U.S. Internship Request for Approval" process found under the myPlans tab in myHill to register for this Internship.

3

### Directed Study

Offered: Fall and Spring Semesters

Opportunity for upper level students to do advanced work in a specialized area of mathematics. Permission of faculty member directing the project and the department chairperson required.

3

### Independent Research

Offered: Fall and Spring Semesters

Students carry out an independent research project under the direction of a faculty member. The research may be part of an ongoing project being conducted by the faculty member, or the student and faculty member may develop an original project.

3

## Note

It is strongly recommended that mathematics minors fulfill their natural scientific inquiry and writing-in-the disciplines requirements by taking MTH 191 - The Language of Mathematics (WID), in their freshman or sophomore year.