# Mathematics, B.S. Requirements

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

The B.S. in Mathematics requires the completion of 16 courses.

## Complete Nine Required Courses

Typically taken Freshmen and Sophomore Years.

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.

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

4

### The Language of Mathematics (WID)

Offered: Fall Semester

Covers basic concepts, reasoning patterns, and the language skills which are fundamental to higher mathematics. These skills include the ability to read and write mathematics, employ common patterns of mathematical thought, and read the write proofs.

Prerequisite(s): MTH 126 or consent of the instructor.
Fulfills the Natural Scientific Inquiry and Writing in the Disciplines requirements.

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.

Prerequisite(s): MTH 261.

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.

Prerequisite(s): MTH 126.

4

### 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

### Computer Science I

Offered: Fall Semester

An introduction to programming and problem solving using Java. Topics include: Input and Output; Selection; Repetition; Methods; Recursion; Arrays; Classes and Objects.

Course may be applied to the Data Science program.

4

### Physics I

Offered: Fall Semester

Brief introduction to vectors and basic concepts of calculus; kinematics; Newton’s laws, force, work and power; conservative forces, potential energy; momentum, collisions; rotational motion, angular momentum, torque; oscillations, simple harmonic motion; gravitation and planetary motion; fluid dynamics; kinetic theory of gases, thermodynamics; heat capacity and transport.

Corequisite(s): MTH 125.

4

### Physics II

Offered: Spring Semester

Brief introduction to the basic concepts of vector calculus, such as line and surface integrals, integral version of Gauss’ theorem and Stokes’ theorem; Coulomb’s law, insulators and metals; electrostatic induction, potential energy; capacitance; currents, resistance, basic circuits, batteries; magnetism and currents; Ampere’s law; motion of free charges in magnetic fields, mass spectroscopy; magnetic induction, Faraday’s law; Maxwell’s equations, electromagnetic waves; geometric and wave optics; light as photons, photoelectric effect.

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

4

Typically taken Junior and Senior Years.

Code Course Credits

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Theory of Computation

Offered: Alternate Years: Fall 2016, 2018

For description and semester schedule see CSC 384.

3

### 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

### 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

### 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

### Topics in Mathematics

Offered: Not Offered 2015-2016

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.

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

3

## Complete a Capstone in Mathematics

Code Course Credits

### Senior Capstone: Mathematical Modeling

Offered: Fall Semester

Students learn to create models of real world phenomena using mathematical tools such as difference equations, differential equations, lineal algebra, and calculus.

Prerequisite(s): Math Major, Senior Standing.

4