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.
Student Learning Goals
The graduating mathematics majors will be able to:
Goal 1: Perform tasks requiring logical reasoning;To meet these learning goals in a manner consistent with the interests and needs of its diverse clientele — mathematics, science and education majors, as well as students in other disciplines — the department offers a variety of courses and programs. Graduates who major in mathematics can enter careers in research, education, industry, business and government, among other fields. Increasingly, they go on to earn advanced degrees in the areas of business, economics, computer science, operations research, statistics and actuarial science, as well as mathematics. The mathematics major is available under three options, each of which furnishes a sound foundation for the future.
Goal 2: Discern patterns, coherence and significance of central mathematical topics and concepts;
Goal 3: Persist through complex reasoning with enthusiasm and curiosity as they explore new mathematical areas;
Goal 4: Learn mathematical content and analyze relevant information;
Goal 5: Communicate mathematical ideas with precision and clarity in both written and oral form.
Option A, the major option, 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, mathematics with a concentration in another area, allows the student to develop expertise in another area besides mathematics. The option may enable a student to earn a dual major or a minor from another department. Students interested in teaching at the secondary or elementary/early secondary level may take advantage of this option to give themselves a strong background in mathematics while fulfilling the requirements of the School of Education.
Option C, the statistics option, prepares the student for advanced work and the many careers which utilize statistical thinking. The course work also offers students good preparation for graduate study.
Option B or C, together with appropriate courses in business, can constitute a good preparation for a career in actuarial science.
The department also offers a mathematics minor, which is described under Other Programs.
For the non-specialist in mathematics, the department offers service courses which provide mathematical techniques necessary in the development of the student’s own field, studies imparting insights into the nature and applications of mathematics generally and courses treating the historical development or logical foundations of the subject.
Qualifications for the major
Math majors must have a minimum grade of “C -” in all courses in the major.
Mathematics Curriculum:
1. Core Curriculum Requirements:
Go to /academics/core.asp for the Core Curriculum requirements. All students complete these requirements as part of their overall Canisius education.
2. Major course requirements:
| Major courses: | ||
| Option A - Mathematics major credits (16 courses) | ||
| Option B - Mathematics with concentration in another area credits (18 courses) | ||
| MAT 111-112 Calculus I and II | 8 credits | |
| MAT 211 Calculus III | 4 credits | |
| MAT 230 Logic, Set Theory and Proofs | 4 credits | |
| MAT 219 Linear Algebra | 4 credits | |
| MAT 222 Differential Equations | ||
| OR MAT 351 Probability and Statistics |
4 or 3 credits | |
| MAT 311 Abstract Algebra I | 4 credits | |
| MAT 321 Real Analysis I | 4 credits | |
| MAT 311 Abstract Algebra I | 3 credits | |
| One course to be chosen from the following: MAT 312, 313, 322, 411, 416, 421 | 3 credits | |
| Mathematics Seminar (MAT 380-381-480) |
3 credits | |
| PHY 223-224 General Physics for Physical Science Majors OR Two Economics courses |
8 or 6 credits | |
| Restricted Major Electives in Options: | ||
| Option A: four additional 300 or 400-level Mathematics courses | 12 credits | |
| Option B: two additional 300 or 400-level Mathematics courses, and four courses in another area approved by the Mathematics Department |
18 credits | |
| Option C (Statistics credits) (16 courses) | ||
| MAT 111-112 Calculus I and II | 8 credits | |
| MAT 211 Calculus III | 4 credits | |
| MAT 230 Logic, Set Theory and Proofs | 4 credits | |
| MAT 219 Linear Algebra | 4 credits | |
| MAT 222 Differential Equations OR Mathematics elective: one 300- or 400-level Mathematics course |
4 or 3 credits | |
| MAT 351-352 Probability and Statistics | 6 credits | |
| MAT 321 Real Analysis I | 4 credits | |
| MAT 322 Real Analysis II OR MAT 311 Abstract Algebra I Mathematics seminar |
3 or 4 credits | |
| PHY 223-224 General Physics for Physical Science Majors OR Two Economics courses |
10 or 6 credits | |
| Restricted major electives: three additional upper-level Mathematics/Statistics courses from (MAT 353, 354, 365, 370) |
9 credits | |
3. Free electives:
Free electives are courses in addition to the Core Curriculum and major requirements sufficient to reach a minimum of 120 credit hours for graduation. Students may graduate with more but not less than 120 credit hours. Note: the Department recommends at least one computer science course, such as CSC 111. Students planning on graduate work in mathematics should take as many as possible from the following: MAT 312, 313, 322, 411, 416, 421
Recommended Semester Schedule for Major Courses (Options A and B):
| Fall | Spring | |||||
| Freshman Year | ||||||
| MAT 111 | 4 credits | MAT 112 | 4 credits | |||
| PHY 223 or Economics | 4 or 3 credits | |||||
| Sophomore Year | ||||||
| PHY 224 or Economics | 4 or 3 credits | Attribute/Elective | 3 credits | |||
| MAT 211 | 4 credits | MAT 219 | 4 credits | |||
| MAT 230 | 4 credits | MAT 222 or 351 | 4 or 3 credits | |||
| Junior Year | ||||||
| MAT 311 | 4 credits | One of these: MAT 312, 313 , 322, 421 | 3 credits | |||
| MAT 321 | 4 credits | Mathematics elective | 3 credits | |||
| Mathematics Seminar | 1 credits | Mathematics Seminar | 1 credits | |||
| Senior Year | ||||||
| Mathematics elective | 3 credits | Mathematics elective | 3 credits | |||
| Mathematics elective | 3 credits | |||||
| Mathematics Seminar | 1 credits | |||||
Recommended Schedule (Option C):
| Fall | Spring | |||||
| Freshman Year | ||||||
| MAT 111 | 4 credits | MAT 112 | 4 credits | |||
| RST 101 or PHI 101 | 3 credits | PHY 223 or Economics | 4 or 3 credits | |||
| Sophomore Year | ||||||
| PHY 224 or Economics | 4 or 3 credits | MAT 219 | 4 credits | |||
| MAT 211 | 4 credits | MAT 351 | 3 credits | |||
| MAT 230 | 4 credits | |||||
| Junior Year | ||||||
| MAT 321 | 4 credits | MAT 322 OR MAT 222/ Math Elective | 3 or 4 credits | |||
| MAT 352 | 4 credits | Statistics elective | 3 credits | |||
| Mathematics Seminar | 1 credits | Mathematics Seminar | 1 credits | |||
| Senior Year | ||||||
| Statistics elective | 3 credits | MAT 222/Math elective | 4 or 3 credits | |||
| MAT 311 or Math Elective | 3 credits | Statistics elective | 3 credits | |||
| Mathematics Seminar | 1 credits | |||||
Other Programs
Mathematics Minor: (7 courses)
| MAT 111 Calculus I OR MAT 115 Calculus for Business I | 4 credits | |
| MAT 112 Calculus II | 4 credits | |
| MAT 211 Calculus III | 4 credits | |
| MAT 219 Linear Algebra | 4 credits | |
| MAT 230 Logic, Set Theory and Proofs | 4 credits | |
| Restricted electives: two courses from any one of the following tracks: |
6-8 credits | |
| Probability and Statistics: MAT 351, 352, 353, 354, 365, 390 | ||
| Applied Mathematics: MAT 222, 335, 336, 341 | ||
| Theoretical Mathematics: MAT 311, 312, 313, 321, 322. 411, 416, 421 |
||
| Mathematics and Culture: MAT 301, 331 | ||
Dual Major or Minor in Another Department
By suitable choice of electives, a student following Option B can also complete the requirements for a minor or a major in another department, most commonly physics, chemistry, computer science or economics.
Additional Information
Students of computer science, physics, chemistry and engineering, in consultation with their advisors, should consider taking MAT 219 (Linear Algebra), even if this course is not listed as a required course in their major. Increasingly, linear algebra is playing an important role in applications of mathematics. This recommendation is in addition to the required calculus courses so central to the understanding of many physical, biological, chemical and economic phenomena. Those interested in probability and statistics are encouraged to take MAT 351-352.
COURSES: 2009 - 2011
MAT 002 Pre-College Mathematics II 0 credits
Intermediate Algebra II: Simplifying and solving rational equations, conic sections, relations and functions, exponential and logarithmic functions. Word problems. Fall
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. (Field 7) Fall & Spring
MAT 106 Calculus for the Non-Sciences I 3 credits
Fundamentals of calculus for students in business, or social or behavioral sciences. Credit not allowed if student already has credit for MAT 111 or 115. (Field 7) Fall & Spring
MAT 107 Calculus for the Non-Sciences II 3 credits
Continuation of MAT 106. Integral calculus and calculus of several variables with applications. (Field 7). On demand
MAT 109-110 Calculus with Review I and II 4-4 credits
For science and mathematics majors. Calculus, with topics from pre-calculus. Logarithms, exponentials, trigonometric functions, limits, differentiation, related rates, max-min problems, anti-differentiation, definite integral. No credit allowed if student has credit for MAT 111, 115 or 117. (Field 7) MAT 109 Fall; MAT 110 Spring
MAT 111 Calculus I 4 credits
For science and mathematics majors. Functions of single variable. Functions, limits, differentiation, continuity, graphing, logarithm, exponential and inverse trigonometric functions, related rates, max-min problems, mean value theorem, l’Hospital’s rule, anti-differentiation, definite integral. (Field 7) Fall & Spring
MAT 112 Calculus II 4 credits
Applications of integration. Integration techniques, improper integrals, sequences, series, convergence tests, Taylor’s theorem, applications; parametric and polar curves. (Field 7) Prerequisite: MAT 111 or 115 with minimum grade C-. Fall & Spring
MAT 115 Calculus for Business I 4 credits
First of two semesters of mathematics for business students. Differentiation/integration of functions of one variable. Applications: concepts, examples and problems in economicsand business. (Field 7) Prerequisite: 3 1/2 years of high school mathematics. Fall
MAT 121 The Nature of Mathematics 3 credits
Liberal arts mathematics course. Problem solving techniques, deductive reasoning in mathematics, some modern topics and quantitative thinking. (Field 7) Prerequisite: 3 years of high school math or equivalent; sophomore standing or higher. Spring
MAT 131 Statistics and Computers 3 credits
A first course for majors in social or health sciences. Descriptive statistics, calculators, computer programs and introduction to inferential statistics. (Field 7) Prerequisite: High school intermediate algebra. 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. (Field 7) Prerequisite: 3-1/2 years of high school mathematics. 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. (Field 7) Prerequisite: 3 years of high school mathematics or equivalent. Spring
MAT 181 Symmetry 3 credits
Liberal arts course exploring the mathematical world of geometry and symmetry. Measurement, billiards, polygons and polyhedra, tilings and wallpaper patterns, spirals and natural growth. (Field 7) Prerequisite: 3 years of high school mathematics or equivalent. Fall
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, graphs. Prerequisite: Sophomore standing or instructor's permission. Spring
MAT 211 Calculus III 4 credits
Continuation of MAT 111-112. Analytic geometry of 3-space and calculus of functions of several variables. Prerequisite: MAT 112 with minimum grade of C -. 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 consent of the instructor. Fall & Spring
MAT 222 Differential Equations 4 credits
Introduction to the theory and applications of ordinary differential equations. Prerequisite: MAT 211 with minimum grade of C -. 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: MAT 112 with minimum grade of C - or consent of the instructor. Fall & Spring
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 111-112. Fall 2010
MAT 311 Abstract Algebra I 4 credits
Introduction to the basic structures of abstract algebra; groups, rings, fields. Prerequisites: MAT 230 and MAT 219 with minimum grades of C -. Fall
MAT 312 Abstract Algebra II 3 credits
Continuation of MAT 311. Selected topics from rings, Integral domains, field extensions and Galois theory. Prerequisite: MAT 311. Spring 2011
MAT 313 Number Theory 3 credits
Divisibility, prime numbers, numerical functions, congruencies, quadratic reciprocity, Diophantine equations. Prerequisite: MAT 311 or permission of instructor. Spring 2010
MAT 321 Real Analysis I 4 credits
Advanced study of differentiation and integration of functions. Prerequisites: MAT 211, 230, 219 with minimum grades of C -; or MAT 211, 230 and consent of instructor. Fall
MAT 322 Real Analysis II 3 credits
Continuation of MAT 321. Selected topics from functions of one or several variables. Prerequisite: MAT 321 with minimum grade of C -. Spring 2010
MAT 331 Introduction to Modern Geometry 3 credits
Axioms for geometry and their consequences: independence of the parallel postulate. Rudiments of hyperbolic geometry. Geometric transformations. Prerequisite: MAT 230. Fall
MAT 335-336 Mathematical Analysis for Physicists 4-4 credits
Theory and applications of infinite series. Fourier series, Green’s functions. Fourier integrals, vector calculus, linear algebra, partial differential equations and complex variables. Prerequisite: MAT 222 or consent of instructor.
MAT 341 Numerical Analysis 3 credits
The methods used to obtain numerical solutions of functional, integral and differential equations. Prerequisites: An elementary knowledge of computer programming and MAT 219. On demand
MAT 342 (CSC 342) Introduction to 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: one semester of Calculus. On demand
MAT 351-352 Probability and Statistics 3-3 credits
Introduction to the mathematical aspects of modern probability theory and the theory of statistics. Prerequisite: MAT 211.MAT 351 Spring; MAT 352 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. Prerequisites: MAT 351-352 or consent of instructor. Spring 2010
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. Prerequisites: MAT 351-352 or permission of instructor. Fall 2009
MAT 365 Logistic Regression 3 credits
Statistical analysis of dichotomous data. Univariate and multivariate cases are covered. Applied problems solved on the computer. Prerequisite: MAT 352 or ECO 256. Fall 2010
MAT 370 Topics in Statistics 3 credits
Prerequisite: MAT 352 or permission of instructor. Spring 2011
MAT 380-381-480 Mathematics Seminar 1 credit each
Mathematics seminar for majors To be taken for three semesters. Prerequisite: Junior standing
MAT 400 (PHY 400) Math/Physics Reading Group 1 credit
Study of a book on recent developments in math and science. Book subject varies. May be taken more than once. Prerequisite: By permission. On demand
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 or permission of instructor. Fall 2011
MAT 416 Differential Geometry 3 credits
Curves in the plane and 3 space: Frenet formulas, isoperimetric inequalities. Basic elements of surface theory. Curvature and mean curvature. Gauss’s Theorema Egregium. Rigidity questions. Prerequisite: MAT 321. On demand
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, Rouch’s Theorem. Prerequisite: MAT 321 or permission of the instructor. Spring 2011
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. Prerequisite: Consent of chair. On demand
MAT 499 Independent Study 3 credits
Prerequisite: Consent of instructor and chair. On demand