## Mathematics – B.A.

## Program Description

The Department supports two mathematics majors, one leading to a B.A. and another leading to a B.S. The B.A. track offers more flexibility and the ability to focus on coursework relevant to a student's career goals. Students in the B.A. track often pursue a minor or a second major in a related field. The B.S. track is better suited for students who wish to pursue mathematics at the graduate level after graduation.

### Mission Statement

Our mission is in accord with the mission of the University. Learning has the highest priority in the Mathematics program. Our mission is to help our students to observe reality with precision, to think logically, and to communicate effectively. With the ultimate goal of developing our students as self-learners, members of our faculty strive to research and implement teaching strategies that effectively serve the mathematics population.

Students should leave La Salle prepared to enter professional fields that utilize their mathematics education. In addition, students who demonstrate the ability and determination to continue academically will be prepared to pursue graduate studies. We expect that participants in our programs, both students and faculty, will expand their thirst for learning and develop a deeper appreciation and respect for related disciplines. To these ends, we work to provide a classical foundation in the core of the discipline, introduce current theories, research areas, and technologies, and demonstrate the links between theory and its embodiment in the world of applications.

## Why take this major?

The mathematics major helps one to think logically, to formulate complex problems in a well-defined manner, to critically analyze data, and to determine optimal solutions to real-world problems. All of these skills are transferable to a wide variety of careers that make mathematicians highly sought after in the work force. Mathematics majors often pursue careers as actuaries, statisticians, financial analysts, and teachers, but they are also well-prepared to enter the workforce in a much wider range of career fields.

## Student Learning Outcomes

Upon completion of the program, students will be able to:

- demonstrate competency in the areas that comprise the core of the mathematics major
- demonstrate the ability to understand and write mathematical proofs
- be able to use appropriate technologies to solve mathematical problems
- be able to construct appropriate mathematical models to solve a variety of practical problems

## Program Contact Information

Department of Mathematics and Computer Science

Holroyd Hall 123

(215) 951-1130

Jonathan Knappenberger, Ph.D.

Chair, Mathematics and Computer Science

knappenb@lasalle.edu

Kelley Tuman

Administrative Assistant I

tuman@lasalle.edu

## Degree Earned

B.A.

## Number of Courses Required for Graduation

**Major:** 15

**Total:** 38

## Number of Credits Required for Graduation

**Major:** 52

**Total:** 120

## GPA Required for Graduation

**Major:** 2.0

**Cumulative:** 2.0

## Progress Chart

### Level One - Core Courses

**12 courses and 2 modules required**

#### Universal Required Courses (4 Courses)

**Students must complete the following 4 courses.**

**ILO 8.1: Written Communication**

ENG 110 - College Writing I: Persuasion

**ILO 5.1: Information Literacy**

ENG 210 - College Writing II: Research

**ILO 1.1: Understanding Diverse Perspectives**

FYS 130 - First-Year Academic Seminar **

*NOTE. The following students use *Level 2 Capstone Experience in Major* instead of *FYS 130:* Honors, BUSCA, Core-to-Core, Transfer, and Non-Traditional/Evening.*

**ILO 2.1: Reflective Thinking and Valuing**

REL 100 - Religion Matters

#### Elective Core Courses (4 Courses)

Students must complete 1 course in each of the following 4 ILOs.

**ILO 3.1a: Scientific Reasoning**

PHY 105 - General Physics I

**ILO 3.1b: Quantitative Reasoning**

MTH 120 - Calculus I

**ILO 6.1: Technological Competency**

CSC 230 - Programming Concepts and User Interfaces or CSC 280 - Object Programming

**ILO 8.1a/12.1: Oral Communication/ Collaborative Engagement**

Choose course within ILO

#### Distinct Discipline Core Courses (4 Courses)

**Students must complete 1 course in each of the following 4 ILOs. Each course must be from a different discipline. (A "discipline" is represented by the 3- or 4-letter prefix attached to each course.)**

**ILO 4.1: Critical Analysis and Reasoning**

Choose course within ILO

**ILO 9.1: Creative and Artistic Expression**

Choose course within ILO

**ILO 10.1: Ethical Understanding and Reasoning**

Choose course within ILO

**ILO 11.1: Cultural and Global Awareness and Sensitivity**

Choose course within ILO

#### Universal Required Modules (2 Courses)

**Students must complete the following 2 non-credit modules.***The Modules are not required for Transfer Students, Core-to-Core Students, or BUSCA Students. BUSCA students are required to take modules if/when they pursue a bachelor’s degree.*

**ILO 7.1a**

Health Literacy Module

**ILO 7.1b**

Financial Literacy Module

### Major Requirements

**Major requirements include 4 ****Level Two ILO requirements****, fulfilled through the major.**

Students in this major must complete **38** courses in total in order to graduate. **15** courses will be from this major program.

#### Level Two (4 Courses)

**Students must complete 1 course/learning experience in each of the 4 commitments.**

**ILO 2.2: Broader Identity (Capstone Course/Experience)**

MTH 322 - Differential Equations

**Choose one ILO from 3.2a, 3.2b, 4.2, 5.2, 6.2, 7.2a, or 7.2b: Expanded Literacies**

MTH 341 - Abstract Algebra

**ILO 8.2b: Effective Expression (Writing-Intensive Course)**

MTH 302 - Foundations of Math

**Choose on ILO from 10.2, 11.2, or 12.2: Active Responsibility**

MTH 410 - Probability

#### All Other Required Courses

MTH 120 - Calculus I

MTH 121 - Calculus II

MTH 222 - Calculus III

MTH 240 - Linear Algebra

MTH 302 - Foundations of Mathematics

MTH 322 - Differential Equations

MTH 341 - Abstract Algebra

MTH 410 - Probability

Five MTH electives numbered 300 or higher

PHY 105 - General Physics I

CSC 230 - Programming Concepts and User Interfaces or CSC 280 - Object Programming

#### Free Electives

**In addition to the requirements listed above, students must take enough courses to the fulfill graduation credit requirements for their School and major.**

## Dual Major Requirements

Students in the Mathematics BA program will often pursue a second major, and doing so is encouraged and supported by the department. Fields in which students often pursue a second major include Computer Science, Economics, Finance, Chemistry, and Education. The required course for the dual major in Education are listed below. Please see the Department Chair regarding the requirements for other potential dual majors.

### Required for Majors in Mathematics-Education

**12+ Courses**

- MTH 120 - Calculus I
- MTH 121 - Calculus II
- MTH 222 - Calculus III
- MTH 240 - Linear Algebra
- MTH 302 - Foundations of Mathematics
- MTH 330 - Modern Geometries
- MTH 341 - Abstract Algebra
- MTH 405 - History of Mathematics
- MTH 410 - Probability
- CSC 230 - Programming Concepts and User Interfaces or CSC 280 - Object Programming
- PHY 105 - General Physics I
- One MTH elective numbered 300 or higher
- Additional courses as specified by the Education Department

## Minor Requirements

**Required for a Minor in Mathematics: 6 Courses**

**MTH 120 - Calculus I****MTH 121 - Calculus II**- Any three from
**MTH 222, MTH 240,****MTH 302,****MTH 322** - One additional Mathematics course numbered 300 or greater.

## Recommended Course Sequence

Students should complete the Calculus sequence (MTH 120/121/222) within their first three semesters. Additionally, MTH 240 and MTH 302 should be taken during the sophomore year. Many upper-division courses rely on the knowledge from MTH 302, so it is important to take this course prior to the junior year.

## Course Descriptions

### CSM 154 - Mathematical Technology

This course focuses on the use of technology as a tool for solving problems in mathematics, learning mathematics and building mathematical conjectures; electronic spreadsheets, a Computer Algebra System (CAS), and a graphing calculator; the use of these tools, programming within all three environments, including spreadsheet macros, structured CAS programming, and calculator programming. A TI-89 graphing calculator is required.

*Number of Credits:* 4

*How Offered:* Face-to-Face

### MTH 101 - College Algebra

Topics include functions and graphs; equations and inequalities; systems of equations; polynomial, rational, exponential, and logarithmic functions. Students who have other college credits in mathematics must obtain permission of the department chair to enroll in this course.

*Number of Credits:* 3

*When Offered:* Fall, Spring

*How Offered:* Face-to-Face

### MTH 114 - Applied Business Calculus

An introduction to mathematical modeling and single-variable differential calculus with an emphasis on data analysis and applications to business and economics. Topics include modeling data using polynomial, exponential, and logarithmic functions; rates of change; derivative rules, including the Product Rule and Chain Rule; applications of derivatives. Applications include compound interest; revenue, cost, profit, average cost; break-even analysis; elasticity of demand; marginal cost; optimization; concavity and inflection points. A TI graphing calculator is required.

*Number of Credits:* 4

*When Offered:* Fall, Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 101 or a Mathematics Placement of 102M

*ILO Met:* ILO 3.1.b - Quantitative Reasoning

### MTH 119 - Precalculus

This course provides a review of algebra and trigonometry as a preparation for courses in the calculus sequence. Topics include: exponents and radicals; polynomials and rational expressions; factoring; division with polynomials; solving equations and inequalities in one variable; graphing in the coordinate plane; linear, quadratic, and higher-degree polynomial functions; horizontal and vertical transformations of functions; rational zeros of functions; exponential and logarithmic functions and their graphs; laws of logarithms; solving exponential and logarithmic equations; radian and degree measure; reference angles; trigonometric functions and graphs; right triangle trigonometry; trigonometric identities and formulas; solving trigonometric equations. A TI graphing calculator is required.

*Number of Credits:* 4

*When Offered:* Fall, Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 101 or a Mathematics Placement of 102M

### MTH 120 - Calculus I

Topics in this course include functions of various types: rational, trigonometric, exponential, logarithmic; limits and continuity; the derivative of a function and its interpretation; applications of derivatives, including finding maxima and minima and curve sketching; antiderivatives, the definite integral and approximations; the fundamental theorem of calculus; and integration using substitution. A TI graphing calculator is required.

*Number of Credits:* 4

*When Offered:* Fall, Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 119 or its equivalent

*ILO Met:* ILO 3.1.b - Quantitative Reasoning

### MTH 121 - Calculus II

This course addresses differentiation and integration of inverse trigonometric and hyperbolic functions; applications of integration, including area, volume, and arc length; techniques of integration, including integration by parts, partial fraction decomposition, and trigonometric substitution; L'Hopital's Rule; improper integrals; infinite series and convergence tests; Taylor series; parametric equations; polar coordinates; and conic sections. A TI graphing calculator is required.

*Number of Credits:* 4

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 120

### MTH 150 - Mathematics: Myths and Realities

This course offers an overview of mathematical concepts that are essential tools in navigating life as an informed and contributing citizen, including logical reasoning, uses and abuses of percentages, financial mathematics (compound interest, annuities), linear and exponential models, fundamentals of probability, and descriptive statistics. Applications include such topics as population growth models, opinion polling, voting and apportionment, health care statistics, and lotteries and games of chance.

*Number of Credits:* 3

*When Offered:* Fall, Spring, Summer

*How Offered:* Face-to-Face

*ILO Met:* ILO 3.1.b - Quantitative Reasoning

### MTH 222 - Calculus III

This course addresses three-dimensional geometry, including equations of lines and planes in space, and vectors. It offers an introduction to multi-variable calculus including vector-valued functions, partial differentiation, optimization, and multiple integration. Applications of partial differentiation and multiple integration. A TI-89 graphing calculator is required.

*Number of Credits:* 4

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 121

### MTH 240 - Linear Algebra

This course includes vectors and matrices, systems of linear equations, determinants, real vector spaces, spanning and linear independence, basis and dimension, linear transformations, eigenvalues and eigenvectors, and orthogonality. Applications in mathematics, computer science, the natural sciences, and economics are included.

*Number of Credits:* 4

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 120

### MTH 260 - Discrete Structures I

This course is the first half of a two-semester course in discrete mathematics and is intended for computer science and information technology majors. Topics in the course include logic, sets, functions, numeric bases, matrix arithmetic, divisibility, modular arithmetic, elementary combinatorics, probability, graphs, and trees. There will be an emphasis on applications to the broad field of computing.

*Number of Credits:* 3

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 101 or a Mathematics Placement of 102M

*ILO Met:* ILO 3.1.b - Quantitative Reasoning

### MTH 261 - Discrete Structures II

This course is the second half of a two-semester course in discrete mathematics and is intended for computer science majors. Topics in the course include rules of inference, proof methods, sequences and summation, growth of functions, complexity of algorithms, prime numbers and their application to cryptography, proof by induction, recursion, recurrence relations, and properties of relations. There will be an emphasis on applications to computer science.

*Number of Credits:* 3

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 260

### MTH 302 - Foundations of Mathematics

Topics in this course include propositional logic, methods of proof, sets, fundamental properties of integers, elementary number theory, functions and relations, cardinality, and the structure of the real numbers.

*Number of Credits:* 3

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 120

*Corequisites:* MTH 121

### MTH 322 - Differential Equations

This course focuses on analytical, graphical, and numerical techniques for first and higher order differential equations; Laplace transform methods; systems of coupled linear differential equations; phase portraits and stability; applications in the natural and social sciences. (offered in alternate years)

*Number of Credits:* 4

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 121

### MTH 330 - Modern Geometries

Topics from Euclidean geometry including: planar and spatial motions and similarities, collinearity and concurrence theorems for triangles, the nine-point circle and Euler line of a triangle, cyclic quadrilaterals, compass and straightedge constructions. In addition, finite geometries and the classical non-Euclidean geometries are introduced. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 240 or MTH 302

### MTH 335 - Graph Theory

This course introduces students to the field of graph theory and leads them through an exploration of the major branches of this subject, incorporating both theoretical results and current applications for each area studied. From a theoretical perspective, students re-derive well-known existing results and construct proofs related to new topics which have been introduced. From an applied standpoint, members of the class learn to formulate graph models to solve problems in computer science, the natural sciences, engineering, psychology, sociology, and other fields. We also consider some open problems and pose new questions of our own. In addition to fundamental definitions and concepts in graph theory, some specific topics that will be introduced are the following: Eulerian, Hamiltonian, planar, and directed graphs; trees, connectivity, matching, decomposition, coloring, covering, and independent sets and cliques; techniques and algorithms on graphs; and optimization problems and network flows.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Restrictions:* junior mathematics standing or permission of the department chair

### MTH 341 - Abstract Algebra

Sets and mappings; groups, rings, fields, and integral domains; substructures and quotient structures; homomorphisms and isomorphisms; abelian and cyclic groups; symmetric and alternating groups; polynomial rings are topics of discussion in this course. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 302

### MTH 345 - Combinatorics

This course addresses permutations and combinations, generating functions, recurrence relations and difference equations, inclusion/exclusion principle, derangements, and other counting techniques, including cycle indexing and Polya's method of enumeration.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Prerequisites:* MTH 121

### MTH 370-379 - Selected Topics in Mathematics

This is an introductory course to specialized areas of mathematics. The subject matter will vary from term to term.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Restrictions:* junior or senior standing

### MTH 405 - History of Mathematics

This course is an in-depth historical study of the development of arithmetic, algebra, geometry, trigonometry, and calculus in Western mathematics (Europe and the Near East) from ancient times up through the 19th century, including highlights from the mathematical works of such figures as Euclid, Archimedes, Diophantus, Fibonacci, Cardano, Napier, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, and Gauss. A term paper on some aspect of the history of mathematics is required. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 302

### MTH 410 - Probability

Topics in this course include sample spaces and probability measures, descriptive statistics, combinatorics, conditional probability, independence, random variables, joint densities and distributions, conditional distributions, functions of a random variable, expected value, variance, various continuous and discrete distribution functions, and the Central Limit Theorem. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Fall

*How Offered:* Face-to-Face

*Prerequisites:* MTH 222

### MTH 411 - Mathematical Statistics

Topics in this course include measures of central tendency and variability, random sampling from normal and non-normal populations, estimation of parameters, properties of estimators, maximum likelihood and method of moments estimators, confidence intervals, hypothesis testing, a variety of standard statistical distributions (normal, chi-square, Student's t, and F), analysis of variance, randomized block design, correlation, regression, goodness of fit, and contingency tables. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 410

### MTH 421 - Numerical Analysis

A survey of numerical methods commonly used in algebra and calculus with emphasis on both algorithms and error analysis. Topics include round-off error, numerical methods for solving equations in one variable, interpolation and polynomial approximation, and numerical differentiation and integration. Methods and techniques studied include Bisection, Fixed-Point Iteration, Newton’s Method, Müller’s Method, Lagrange Polynomials, Neville’s Method, Divided Differences, Cubic Splines, Three-point and Five-point Numerical Differentiation Formulas, Newton-Cotes Formulas, Composite Numerical Integration, Adaptive Quadrature, Gaussian Quadrature.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Prerequisites:* MTH 121

### MTH 424 - Complex Variables

This course examines analytic functions; Cauchy-Riemann equations; Cauchy's integral theorem; power series; infinite series; calculus of residues; contour integration; conformal mapping.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Prerequisites:* MTH 222

### MTH 425 - Mathematical Modeling

This course addresses the uses of mathematical methods to model real-world situations, including energy management, assembly-line control, inventory problems, population growth, predator-prey models. Other topics include: least squares, optimization methods interpolation, interactive dynamic systems, and simulation modeling.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Prerequisites:* MTH 121

### MTH 430 - Topology

Topics in the course include topological spaces; subspaces; product spaces, quotient spaces; connectedness; compactness; metric spaces; applications to analysis. (offered in alternate years)

*Number of Credits:* 3

*When Offered:* Spring

*How Offered:* Face-to-Face

*Prerequisites:* MTH 302

### MTH 470-479 - Selected Topics in Mathematics

This course is an introduction to specialized research, concentrating on one particular aspect of mathematics. The subject matter will vary from term to term.

*Number of Credits:* 3

*How Offered:* Face-to-Face

*Restrictions:* junior or senior standing