Mathematics Minor Requirements

Department Chairperson:Hsin-hao Su Office: Duffy Academic Center 231 Phone: 508-565-1242hsu@stonehill.edu

The minor in Mathematics requires the completion of eight courses.

Complete Five Required Courses

Code Course Credits

MTH 125

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

MTH 126

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.

Prerequisite(s): Prerequisite for MTH 126: MTH 125.

4

MTH 251

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.

Prerequisite(s): MTH 261.

4

MTH 261

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.

Prerequisite(s): MTH 126.

4

MTH 270

Discrete Mathematics

Offered: Spring Semester

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

Prerequisite(s): MTH 191 or instructor permission.

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

MTH 351

Abstract Algebra I

Offered: Fall Semester

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

Prerequisite(s): MTH 270

3

MTH 352

Abstract Algebra II

Offered: Spring Semester

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

Prerequisite(s): MTH 351.

3

MTH 361

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.

Prerequisite(s): MTH 261 and MTH 191

3

MTH 362

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.

Prerequisite(s): MTH 361.

3

MTH 363

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.

Prerequisite(s): MTH 251, MTH 261.

3

MTH 364

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.

Prerequisite(s): MTH 261.

3

MTH 371

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.

Prerequisite(s): MTH 270.

3

MTH 377

Number Theory

Offered: Alternate Years: Spring 2017, 2019

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

Prerequisite(s): MTH 251 and MTH 270.

3

MTH 384

Theory of Computation

Offered: Alternate Years: Fall 2016, 2018

For description and semester schedule see CSC 384.

3

MTH 393

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.

Prerequisite(s): MTH 251 and MTH 261.

3

MTH 395

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.

Prerequisite(s): MTH 251 and MTH 261.
Fulfills the Statistical Reasoning General Education requirement.

3

MTH 396

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.

Prerequisite(s): MTH 395.
Fulfills the Statistical Reasoning requirement. Course may be applied to the Data Science program.

3

MTH 399

Topics in Mathematics

Offered: Not Offered 2015-2016

3

MTH 475

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

MTH 490

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

MTH 496

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.

Prerequisite(s): Approval of the faculty member and the Department Chairperson.

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.