Mathematics and Statistics

Chair: Byung-Jay Kahng, PhD

Introduction

The Department of Mathematics and Statistics strives to transmit an understanding and appreciation of mathematics: its substance, its applicability, its literature, its current directions and problems, its historical development, its human worth and values; and to promote the development of skill in the practice of mathematics. For a more detailed description of the program, faculty, facilities, academic and co-curricular opportunities please go to the Mathematics and Statistics website.   

Qualifications

Students must maintain a 2.0 GPA in their major and a 2.0 overall average to graduate with a degree in Mathematics and Statistics. Students must have a minimum grade of C- in all courses in the major.

Advisement

All students should have an advisor in the major and should contact the department directly to have an advisor assigned if they do not already have one.  Meetings with academic advisors are required prior to students receiving their PIN for course registration each semester. All majors should work closely with their advisor in discussing career expectations, choosing their major electives, developing their entire academic program and planning their co-curricular or supplemental academic experiences.

Dual Majors

Students who wish to expand their educational opportunities may decide to declare a dual major. The decision may be based on career goals or planned graduate studies. Before a student declares a dual major, it is important to meet with the appropriate academic departments for advisement. Some dual major combinations can be completed within the minimum 120 credit hour degree requirement, but in some cases additional course work may be required. In order to declare a dual major, the student must complete the appropriate dual major request form and get the signature of each department chairperson and the appropriate associate dean.

 Popular double majors with mathematics are economics, computer science, education, and physics, but we have also had students double major in math and music, English, political science, philosophy, Spanish, psychology, pre-medicine, and other fields.

Minors in other dISCIPLINES

Minors provide students the opportunity to pursue additional interests but generally do not require as many courses as a major.  Minors generally range from five to eight required courses. The minors page provides a complete list of minors and provides links to each minor. Some majors and minors can be completed within the minimum 120 credit hour degree requirement, but in some cases additional coursework may be required. Students must complete the appropriate minor request form.

Curriculum

An Ignatian Foundation

All undergraduate students must complete either the Canisius Core Curriculum or the All-College Honors Curriculum. Many schools refer to their college-wide undergraduate requirements as "general education" requirements. We believe that the core curriculum and the honors curriculum are more than a series of required classes, they provide the basis for a Jesuit education both with content and with required knowledge and skills attributes that are central to our mission.

Free Electives

Students may graduate with more but not less than 120 credit hours. Free electives are courses in addition to the Core Curriculum or Honors Curriculum and major requirements sufficient to reach the minimum of 120 credit hours required for graduation.

Major Requirements

Option A (Mathematics Major)

MAT 111Calculus I4
MAT 112Calculus II4
MAT 211Calculus III4
MAT 219Linear Algebra4
MAT 222Differential Equations3
or MAT 351 Probability & Statistics I
MAT 230Logic, Set Theory, and Proofs4
MAT 311Abstract Algebra4
MAT 321Real Analysis4
MAT 380Mathematics Seminar1
MAT 381Mathematics Seminar1
MAT 480Mathematics Seminar1
Select one of the following:3
Topics in Algebra
Topics in Analysis
Probability & Statistics II
Select four courses from the following:12-16
Any additional 300 or 400-level mathematics courses
Mathematical Analysis for Physicists
Quantum Mechanics I
Total Credits49-53

Option B (Mathematics with a Concentration in Another Area)

MAT 111Calculus I4
MAT 112Calculus II4
MAT 211Calculus III4
MAT 219Linear Algebra4
MAT 222Differential Equations3
or MAT 351 Probability & Statistics I
MAT 230Logic, Set Theory, and Proofs4
MAT 311Abstract Algebra4
MAT 321Real Analysis4
MAT 380Mathematics Seminar1
MAT 381Mathematics Seminar1
MAT 480Mathematics Seminar1
Select one of the following:3
Topics in Algebra
Topics in Analysis
Probability & Statistics II
Select two of the following:6-8
any additional 300 or 400-level mathematics courses
Mathematical Analysis for Physicists
Quantum Mechanics I
Total Credits43-45

Option C (Statistics)

MAT 111Calculus I4
MAT 112Calculus II4
MAT 211Calculus III4
MAT 219Linear Algebra4
MAT 222Differential Equations (or 300 or 400-level mathematics course)3
MAT 230Logic, Set Theory, and Proofs4
MAT 321Real Analysis4
MAT 322Topics in Analysis3-4
or MAT 311 Abstract Algebra
MAT 351Probability & Statistics I3
MAT 352Probability & Statistics II3
MAT 380Mathematics Seminar1
MAT 381Mathematics Seminar1
MAT 480Mathematics Seminar1
Select three of the following:9
Numerical Analysis
Regression Analysis
Experimental Design and Statistical Computing
Topics in Statistics
Total Credits48-49

Major Electives

Option A

Select one of the following:6
General Physics for Physical Science Majors I
and General Physics for Physical Science Majors II
Two economics courses
Total Credits6

Option B

Select one of the following:6
General Physics for Physical Science Majors I
and General Physics for Physical Science Majors II
Two economics courses
Four courses in another area approved by the Department of Mathematics and Statistics
Total Credits6

Option C

Select one of the following:6
General Physics for Physical Science Majors I
and General Physics for Physical Science Majors II
Two economics courses
Total Credits6

Additional Course Considerations

Option A is designed to prepare the student for positions in which mathematical competence is sought, as well as for advanced study in graduate school.

Option B allows the student to develop expertise in another area besides mathematics. Many students combine this option with a major or minor in another department. Students interested in education can get a dual major to give them a strong background in mathematics while fulfilling the requirements of the School of Education.

Option C prepares the student for advanced work or graduate study and the many careers which utilize statistical thinking. This option, together with appropriate courses in business, constitutes a good preparation for a career in actuarial science.

Roadmap

Recommended Semester Schedule for Major Courses

Option A

Freshman
FallSpring
MAT 111MAT 112
 PHY 223 (or ECO course)
Sophomore
FallSpring
MAT 211MAT 219
MAT 230MAT 222 or 351
PHY 224 (or ECO course) 
Junior
FallSpring
MAT 311MAT 381
MAT 321MAT elective
MAT 380 
Senior
FallSpring
MAT 480Select one of the following:
MAT elective
MAT elective
 
 MAT elective

Option B

Freshman
FallSpring
MAT 111MAT 112
 PHY 223 (or ECO course)
Sophomore
FallSpring
MAT 211MAT 219
MAT 230MAT 222 or 351
PHY 224 (or ECO course) 
Junior
FallSpring
MAT 311MAT 381
MAT 321MAT elective
MAT 380 
Senior
FallSpring
MAT 480Select one of the following:
MAT elective
 
 

Option C

Freshman
FallSpring
MAT 111MAT 112
 PHY 223 (or ECO course)
Sophomore
FallSpring
MAT 211MAT 219
MAT 230MAT 351
PHY 224 (or ECO course) 
Junior
FallSpring
MAT 321MAT 381
MAT 352Select one of the following:
MAT 380
 
 
MAT elective
 Select one of the following statistics electives:
 
 
 
 
Senior
FallSpring
MAT 480Select one of the following:
MAT 311 (or MAT elective)
Select one of the following statistics electives:
MAT elective
Select one of the following statistics electives:
 
 

Learning Goals & Objectives

Student Learning Goal 1:

Mathematics majors will perform tasks requiring logical reasoning.

Students will:
  • Objective A: Understand the different types of mathematical statements and how they are used, including definitions, axioms, hypotheses, conclusions, theorems, corollaries, lemmata, and conjectures;
  • Objective B: Understand methods of proof.

Student Learning Goal 2

Mathematics majors will know the content of the fundamental fields of mathematics and can perform tasks requiring complex reasoning.

Students will:
  • Objective A: Use basic skills to manipulate expressions;
  • Objective B: Know the basic definitions and theorems of mathematics;
  • Objective C: Be able to perform tasks requiring complex reasoning.

Student Learning Goal 3

Mathematics majors will advance their understanding and knowledge of mathematics and their ability to convey mathematical concepts through currently available technology.

Students will:
  • Objective A (Information Literacy): Use the internet and/or library resources to obtain relevant information concerning historical information or mathematical content in regards to current course or project. Students will be expected to both look up sources and learn to search for their own sources;
  • Objective B (Computation): Use computers or graphing calculators to perform labor-intensive calculations and/or create graphical displays. Programs include, but are not limited to, Excel, Minitab (or other statistical software), and Mathematica (or other software);
  • Objective C (Presentation): Use technology for the purpose of elegantly presenting mathematical ideas, theories or results. Technologies include PowerPoint, Prezzi, Jing, Beamer, Latex, Word, and graphical tools.

Student Learning Goal 4

Mathematics majors will communicate mathematical ideas with precision and clarity.

Students will:
  • Objective A: Present mathematical material in writing;
  • Objective B: Present mathematical material orally.

Minor

Mathematics Minor

(7 courses)

Required Courses
MAT 111Calculus I4
or MAT 115 Calculus for Business
MAT 112Calculus II4
MAT 211Calculus III4
MAT 219Linear Algebra4
MAT 230Logic, Set Theory, and Proofs4
Restricted Electives
Select two courses from any one of the following tracks:6-8
Probability and Statistics:
Probability & Statistics I
Probability & Statistics II
Applied Mathematics:
Differential Equations
Mathematical Analysis for Physicists
Numerical Analysis
Graph Theory
Theoretical Mathematics:
Abstract Algebra
Topics in Algebra
Number Theory
Real Analysis
Topics in Analysis
Mathematics and Culture:
History of Mathematics
Geometry
Total Credits26-28

Courses

MAT 105 Finite Mathematics 3 Credits

Introduction to finite (non-calculus) mathematics and its applications: linear, quadratic, exponential and logarithmic functions and equations; systems of linear equations and linear programming; compound interest problems and annuities.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall & spring.

MAT 106 Calculus for the Non-Sciences 3 Credits

Fundamentals of calculus for students in business, or social or behavioral sciences. Credit not allowed if student already has credit for MAT 109 & MAT 110; or MAT 111 or MAT 115.

Prerequisite: MAT 105

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall & spring.

MAT 108 Precalculus for Sciences 3 Credits

Polynomials and rational, exponential, logarithmic, and trigonometric functions. Solving equations. Graphing functions. Trigonometric identities. Credit not allowed if student already has credit for MAT 109, MAT 111, or MAT 115.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: summer.

MAT 109 Calculus with Review I 4 Credits

For science and mathematics majors. Calculus, with topics from pre-calculus. Logarithmic and exponential functions, trigonometric functions, limits, differentiation. Credit not allowed if student already has credit for MAT 111 or MAT 115.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall.

MAT 110 Calculus with Review II 4 Credits

Continuation of MAT 109. Differentiation, related rates, optimization problems, anti-differentiation, definite integral. Credit not allowed if student already has credit for MAT 111 or MAT 115.

Prerequisite: MAT 109

Offered: spring.

MAT 111 Calculus I 4 Credits

For science and mathematics majors. Calculus of functions of single variable. Functions, limits, differentiation, continuity, graphing, logarithm, exponential and inverse trigonometric functions, related rates, optimization problems, mean value theorem, l'Hospital's rule, anti-differentiation, definite integral. Credit not allowed if student already has credit for MAT 109 and MAT 110 or for MAT 115.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall & spring.

MAT 112 Calculus II 4 Credits

Applications of integration, integration techniques, improper integrals, sequences, series, convergence tests, Taylor's series, applications; parametric and polar curves.

Prerequisite: minimum grade of C- in one of the following MAT 109 & MAT 110, MAT 111 or MAT 115.

Offered: fall & spring.

MAT 115 Calculus for Business 4 Credits

Calculus for business students. Differentiation and integration of functions of one variable. Applications, concepts, examples and problems in economics and business. Credit not allowed if student already has credit for either MAT 109 and MAT 110 or for MAT 111.

Prerequisite: 3 1/2 years of high school mathematics.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall.

MAT 121 Mathematics through History 3 Credits

Liberal arts mathematics course. Tracing the development of mathematical ideas globally and through history, with emphasis on problem solving techniques, quantitative thinking, and deductive reasoning.

Prerequisite: 3 years of high school math or equivalent; sophomore standing or higher.

Fulfills College Core: Field 7 (Mathematical Sciences), Global Awareness

Offered: spring.

MAT 131 Statistics for Social Sciences 3 Credits

A first course for majors in social or health sciences. Descriptive statistics, calculators, computer programs and introduction to inferential statistics. Credit not allowed if student already has credit for MAT 141 or MAT 351.

Prerequisite: 3 years of high school mathematics or equivalent.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall & spring.

MAT 141 Inferential Statistics and Computers for Science 4 Credits

Elementary probability theory, descriptive statistics, hypothesis testing, estimation, correlation and regression. The computer will be used with one of the standard statistical packages. Credit not allowed if student already has credit for MAT 131 or MAT 351.

Prerequisite: 3 1/2 years of high school mathematics.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: fall & spring.

MAT 150 Mathematics and Politics 3 Credits

Liberal arts course emphasizing applications of math in the social sciences. Covers topics such as voting theory, decisions made by groups, measurement of political power.

Prerequisite: 3 years of high school mathematics or equivalent.

Fulfills College Core: Field 7 (Mathematical Sciences), Justice

Offered: spring.

MAT 161 Mathematics for Elementary Teachers 3 Credits

Designed to provide a solid foundation for the mathematical topics encountered in elementary schools. The primary goal is to develop a deep understanding of mathematical concepts so future teachers can teach with knowledge and confidence. The main topics are: problem solving processes and strategies, elementary set theory, the theory behind basic arithmetic, number systems, basic probability and statistics, elementary geometry.

Prerequisite: 3 years of high school mathematics or equivalent.

Fulfills College Core: Field 7 (Mathematical Sciences)

Offered: occasionally.

MAT 191 Introduction to Discrete Mathematics 4 Credits

Fundamental topics with computer science applications. Sets and logic, propositional and predicate calculus, elements of combinatorics and counting, elementary discrete probability, functions and relations, and graphs.

Prerequisite: sophomore standing or instructor's permission.

Offered: spring.

MAT 211 Calculus III 4 Credits

Continuation of MAT 111 and MAT 112. Analytic geometry of 3-dimensional space and calculus of functions of several variables.

Prerequisite: minimum grade of C- in MAT 112.

Offered: fall & spring.

MAT 219 Linear Algebra 4 Credits

Vector spaces and inner product spaces. Linear transformations and matrices. Eigenvectors, eigenvalues, and applications. Orthogonal transformations. Quadratic forms and quadric surfaces.

Prerequisite: MAT 112 or permission of instructor.

Offered: spring.

MAT 222 Differential Equations 3 Credits

Introduction to the theory and applications of ordinary differential equations.

Prerequisite: minimum grade of C- in MAT 211.

Offered: spring.

MAT 230 Logic, Set Theory, and Proofs 4 Credits

Transition from calculus to upper division courses: logic and methods of proof; set theory; relations, orders and functions; number systems; cardinality.

Prerequisite: minimum grade of C- in MAT 112 or permission of instructor.

Offered: fall.

MAT 301 History of Mathematics 3 Credits

Development and interrelations of major areas of mathematics, from ancient to modern times. Emphasis on both historical context and mathematical content. Mathematics as cultural heritage.

Prerequisite: MAT 111 & MAT 112.

Offered: fall of odd-numbered years.

MAT 311 Abstract Algebra 4 Credits

Introduction to the basic structures of abstract algebra; groups, rings, fields.

Prerequisite: minimum grade of C- in both MAT 219 and MAT 230.

Offered: fall.

MAT 312 Topics in Algebra 3 Credits

Continuation of MAT 311. Selected topics from groups, rings, integral domains, field extensions and Galois theory.

Prerequisite: MAT 311.

Offered: spring 2017.

MAT 313 Number Theory 3 Credits

Divisibility, prime numbers, numerical functions, congruencies, quadratic reciprocity, Diophantine equations.

Prerequisite: MAT 311 or permission of instructor.

Offered: occasionally.

MAT 321 Real Analysis 4 Credits

Advanced study of limits, continuity, differentiation and integration of functions.

Prerequisite: minimum grade of C- in MAT 211, MAT 219 & MAT 230.

Offered: fall.

MAT 322 Topics in Analysis 3 Credits

Continuation of MAT 321. Selected topics from functions of one or several variables.

Prerequisite: minimum grade of C- in MAT 321.

Offered: spring 2018.

MAT 331 Geometry 3 Credits

Axioms for geometry and their consequences: independence of the parallel postulate. Rudiments of hyperbolic geometry. Geometric transformations.

Prerequisite: MAT 230.

Offered: fall of even-numbered years.

MAT 341 Numerical Analysis 3 Credits

The methods used to obtain numerical solutions of functional and differential equations. Polynomial interpolation. Various approximation algorithms.

Prerequisite: MAT 219 & an elementary knowledge of computer programming.

Offered: spring 2017.

MAT 342 Graph Theory 3 Credits

This course covers basic constructions on graphs. Complete graphs, bipartite graphs, trees, cycles, and more general graphs are studied along with their combinatorial properties. Euler circuits, Hamilton circuits, spanning trees. Applications of graphs to optimization problems such as the Traveling Salesperson Problem and Construction of the Minimal Spanning Trees.

Prerequisite: MAT 111 or MAT 115.

Offered: spring 2018.

MAT 345 Climate and Sustainability 3 Credits

This course, for majors from all the sciences, develops the use of conceptual models in understanding complicated situations, while illustrating the role of scientific arguments in societal debates about climate change and sustainability. Topics include: the Earth's energy balance, historical data for ocean and atmosphere and temperature and their circulation and oscillation patterns, the carbon cycle and biological systems, and handling large data. The increasingly sophisticated examples explored in the course will introduce the use of various areas of mathematics: linear models and networks, calculus-based dynamical systems, statistics and data assessment, and analysis of periodic phenomena. Students will learn about these topics by seeing simple examples of their use. The last part of the course will center on sustainability issues, and connections to global awareness, diversity, ethics, and justice.

Prerequisite: MAT 111 or equivalent. Restriction: seniors only.

Fulfills College Core: Core Capstone

Offered: occasionally.

MAT 351 Probability & Statistics I 3 Credits

Introduction to the mathematical aspects of modern probability theory and the theory of statistics.

Prerequisite: MAT 211.

Offered: spring.

MAT 352 Probability & Statistics II 3 Credits

Continuation of MAT 351. Introduction to the mathematical aspects of modern probability theory and the theory of statistics.

Prerequisite: MAT351.

Offered: fall.

MAT 353 Regression Analysis 3 Credits

Linear regression and correlation. Covariance, residual sum of squares, residual variance, correlation coefficient, tests of significance for correlation coefficient and for regression coefficients. Non-linear regression.

Prerequisite: MAT 351 & MAT 352, or permission of instructor.

Offered: spring 2017.

MAT 354 Experimental Design and Statistical Computing 3 Credits

Analyzing data; one-way/two-way blocking; chi-square, goodness of fit. Statistical computing package; Monte-Carlo simulation-subset selection, central limit theorem; residual plots.

Prerequisite: MAT 351 & MAT 352, or permission of instructor.

Offered: spring 2018.

MAT 361 Probability for Actuaries 1 Credit

This course prepares students to take Exam P of the Society of Actuaries or Exam 1 from the Casualty Actuary Society. Key probability concepts are reviewed and students learn to apply these tools to problems encountered by actuaries. The course will develop a thorough command of calculus and probability topics. Additionally, a very basic knowledge of insurance and risk management is introduced.

Prerequisite: MAT 211 & MAT 351. Corequisite: MAT 352 or permission of instructor.

Offered: fall.

MAT 362 Financial Mathematics for Actuaries 1 Credit

This course prepares students to take Exam FM of the Society of Actuaries or Exam 2 from the Casualty Actuary Society. It covers interest theory (discrete and continuous) and an introduction to derivative securities.

Prerequisite: MAT 111 & MAT 112 or permission of instructor.

Offered: spring.

MAT 370 Topics in Statistics 3 Credits

Selected topics in applied probability and statistics, and nonparametric statistics.

Prerequisite: MAT 352 or permission of instructor.

Offered: fall 2017.

MAT 380 Mathematics Seminar 1 Credit

Mathematics seminar for majors. To be taken for three semesters.

Prerequisite: junior standing.

Offered: fall & spring.

MAT 381 Mathematics Seminar 1 Credit

Mathematics seminar for majors. To be taken for three semesters.

Prerequisite: junior standing.

Offered: fall & spring.

MAT 411 Topology 3 Credits

An introduction to topology, stressing concrete examples including surfaces. Point-set, geometric and algebraic topology with interconnections and applications.

Prerequisite: MAT 230.

Offered: occasionally.

MAT 421 Complex Analysis 3 Credits

Complex numbers, analytic functions and mappings. Cauchy-Riemann equations, harmonic functions, Cauchy's theorem, integral formula and inequalities. Power series, residues, singularities and zeros, Rouche's Theorem.

Prerequisite: MAT 321.

Offered: occasionally.

MAT 480 Mathematics Seminar 1 Credit

Mathematics seminar for majors. To be taken for three semesters.

Prerequisite: junior standing.

Fulfills College Core: Oral Communication

Offered: fall & spring.

MAT 498 Internship in Mathematics 1-3 Credits

Internship involving non-routine tasks linking academic concepts to practical experience. May be used for free elective credit only. Internships require an application and approval by the associate dean.

Prerequisite: permission of the chair & associate dean.

Offered: occasionally.

MAT 499 Independent Study 1-4 Credits

Study and work with a faculty supervisor. Project to be determined by faculty agreement. Independent studies require an application and approval by the associate dean.

Prerequisite: permission of the instructor, department chair, & associate dean.

Offered: occasionally.