Mathematics/Statistics

Mathematics/Statistics

Courses & Curriculum

Qualifications

You must maintain a 2.0 GPA in your major and a 2.0 overall average to graduate with a degree in Mathematics and Statistics.  You must have a minimum grade of C- in all courses in the major, and you must complete a minimum of 120 credit hours to graduate.

Advisement

You should have an advisor in the major and should contact the department directly to have an advisor assigned if you do not already have one.  You should work closely with your advisor in discussing career expectations, designing your entire academic program, choosing major electives and planning your co-curricular or supplemental academic experiences.

Curricular Requirements for the Major

Core: You must complete the core curriculum requirements as part of your overall Canisius education. View the Core Curriculum requirements,

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. You may graduate with more but not less than 120 credit hours.

Major course requirements

Option A (Mathematics Major)

MAT 111 Calculus I

4 credits

MAT 112 Calculus II

4 credits

MAT 211 Calculus III

4 credits

MAT 219 Linear Algebra

4 credits

MAT 222 Differential Equations 
OR
MAT 351 Probability and Statistics I

3 credits

MAT 230 Logic, Set Theory, and Proofs

4 credits

MAT 311 Abstract Algebra

4 credits

MAT 321 Real Analysis

4 credits

Mathematics Seminar  (MAT 380-381-480)

1-1-1 credits

One of the following three courses:

MAT 312 Topics in Algebra
MAT 322 Topics in Analysis
MAT 352 Probability and Statistics II

3 credits

Four additional courses chosen from 300 or 400-level mathematics courses or PHY 335-336

Option B (Mathematics with a concentration in another area)

MAT 111 Calculus I

4 credits

MAT 112 Calculus II

4 credits

MAT 211 Calculus III

4 credits

MAT 219 Linear Algebra

4 credits

MAT 222 Differential Equations 
OR
MAT 351 Probability and Statistics I

3 credits

MAT 230 Logic, Set Theory, and Proofs

4 credits

MAT 311 Abstract Algebra

4 credits

MAT 321 Real Analysis

4 credits

MAT 380-381-480 Mathematics Seminar

1-1-1 credits

One of the following three courses:

MAT 312 Topics in Algebra
MAT 322 Topics in Analysis
MAT 352 Probability and Statistics II

3 credits

Two additional courses chosen from 300 or 400-level mathematics courses or PHY 335-336

3 credits

Option C (Statistics)

MAT 111 Calculus I

4 credits

MAT 112 Calculus II

4 credits

MAT 211 Calculus III

4 credits

MAT 219 Linear Algebra

4 credits

MAT 222 Differential Equations
OR
a 300 or 400-level mathematics course

3 credits

MAT 230 Logic, Set Theory, and Proofs

4 credits

MAT 321 Real Analysis

4 credits

MAT 322 Topics in Analysis
OR
MAT 311 Abstract Algebra

3 or 4
credits

MAT 351 Probability and Statistics I

3 credits

MAT 352 Probability and Statistics II

3 credits

MAT 380-381-480 Mathematics seminar

1-1-1

THREE of the following five courses

MAT 341 Numerical Analysis
MAT 353 Regression Analysis
MAT 354 Experimental Design and Statistical Computing
MAT 365 Logistic Regression
MAT 370 Topics in Statistics

9 credits


Major Electives

Option A: PHY 223-224 General Physics (4-4) or two economics courses
Option B: PHY 223-224 General Physics (4-4) or two economics courses, four courses in another area approved by the Department of Mathematics and Statistics
Option C: PHY 223-224 General Physics (4-4) or two economics courses

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.

Recommended Semester Schedule for Major Courses

 

FALL

SPRING

FRESHMAN

Option A-B-C

Option A-B-C

 

MAT 111 (4)

MAT 112 (4)

PHY 223 (4) or ECO course

SOPHOMORE

Option A-B-C

Option A-B

 

MAT 211 (4)

MAT 230 (4)

PHY 224 or ECO course

MAT 219 (4)

MAT 222 or 351 (3)

   

Option C

   

MAT 219 (4)

MAT 351 (3)

JUNIOR

Option A-B

Option A-B

 

MAT 311 (4)

MAT 321 (4)

MAT 380 (1)

MAT 381 (1)

MAT elective (3)

 

Option C

Option C

 

MAT 321 (4)

MAT 352 (3)

MAT 380 (1)

MAT 381 (1)

MAT 322 or 222 or MAT elective (3)

Statistics elective: MAT 341 or 353 or 354 or 365 or 370 (3)

SENIOR

Option A

Option A

 

MAT 480 (1)

MAT elective (3)

MAT elective (3)

MAT elective (3)

One of MAT 312 or 322 or 352 (3)

 

Option B

Option B

 

MAT 480 (1)

MAT elective (3)

One of MAT 312 or 322 or 352 (3)

 

Option C

Option C

 

MAT 480 (1)

MAT 311 or MAT elective (3)

Statistics elective: MAT 341 or 353 or 354 or 365 or 370 (3)

MAT 322 or 222 or MAT elective (3)

Statistics elective: MAT 341 or 353 or 354 or 365 or 370 (3)


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. 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. Before a student declares a dual major it is important to meet with the appropriate academic departments for advisement. Many 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.

Mathematics Minor:  (7 courses)

MAT 111 Calculus I OR MAT 115 Calculus for Business

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

Probability and Statistics

MAT 351 Probability and Statistics I

3 credits

MAT 352 Probability and Statistics II

3 credits

 

Applied Mathematics

MAT 222 Differential Equations

3 credits

PHY 335 Mathematical Analysis for Physicists I

4 credits

PHY 336 Mathematical Analysis for Physicists II

4 credits

MAT 341 Numerical Analysis

3 credits

MAT 342 Graph Theory

3 credits

 

Theoretical Mathematics

MAT 311 Abstract Algebra

4 credits

MAT 312 Topics in Algebra

3 credits

MAT 313 Number Theory

3 credits

MAT 321 Real Analysis

4 credits

MAT 322 Topics in Analysis

3 credits

 

Mathematics and Culture

MAT 301 History of Mathematics

3 credits

MAT 331 Geometry

3 credits


Courses: 2015 - 2017

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   3 credits
Fundamentals of calculus for students in business, or social or behavioral sciences. Credit not allowed if student already has credit for MAT 109-110 or MAT 111 or MAT 115. (Field 7) 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. (Field 7) Summer

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, optimization problems, anti-differentiation, definite integral. Credit not allowed if student already has credit for MAT 111 or MAT 115. (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, optimization problems, mean value theorem, l’Hospital’s rule, anti-differentiation, definite integral. Credit not allowed if student already has credit for MAT 109-110 or MAT 115.  (Field 7)  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. (Field 7) Prerequisite: MAT 109-110 or MAT 111 or MAT 115 with minimum grade C-. 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 MAT 109-110 or MAT 111.  (Field 7)  Prerequisite: 3 1/2 years of high school mathematics.  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. (Field 7) (Global Awareness Attribute) 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. Credit not allowed if student already has credit for MAT 141 or MAT 351.  (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. Credit not allowed if student already has credit for MAT 131 or MAT 351.  (Field 7)  Prerequisite: 3-1/2 years of high school mathematics.  Fall and 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 - Justice Attribute)  Prerequisite: 3 years of high school mathematics or equivalent. 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. Fall

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-dimensional 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.  Spring

MAT 222 Differential Equations          3 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

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 2015

MAT 311 Abstract Algebra    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 Topics in Algebra   3 credits
Continuation of MAT 311. Selected topics from rings, Integral domains, field extensions and Galois theory. Prerequisite: MAT 311.   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.  On demand

MAT 321 Real Analysis   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 Topics in Analysis   3 credits
Continuation of MAT 321. Selected topics from functions of one or several variables.  Prerequisite: MAT 321 with minimum grade of C -.  Spring 2016

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.   Fall

MAT 341 Numerical Analysis   3 credits
The methods used to obtain numerical solutions of functional, integral and differential equations.  Polynomial interpolation. Various approximation algorithms. Prerequisites: An elementary knowledge of computer programming and MAT 219.  On demand

MAT 342 (CSC 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.  Spring 2016

MAT 351-352 Probability and Statistics I and II    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.  Fall 2015

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 2016

MAT 361: Actuarial Review I   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. Prerequisites: MAT 111-112, MAT 211, and MAT 351-352 or permission of instructor. Fall

MAT 362: Actuarial Review II    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. Prerequisites: MAT 111-112, MAT 211 and MAT 351-352 or permission of instructor.  Spring

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. On demand

MAT 370 Topics in Statistics   3 credits
Prerequisite: MAT 352 or permission of instructor.  Spring 2016

MAT 380-381-480 Mathematics Seminar       1 credit each
Mathematics seminar for majors to be taken for three semesters. (Oral Communication Attribute) Prerequisite: Junior standing. Fall and 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 or permission of instructor. On demand

MAT 416 Differential Geometry           3 credits
Curves in the plane and 3-dimensional 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, Rouche’s Theorem. Prerequisite: MAT 321 or permission of the instructor.  On demand

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