Mathematics Education
The paradigm below is one example of how this major may be completed. Students may use their elective credits to explore other majors or to enroll in skillbuilding courses in mathematics, reading, writing and/or study skills. With planning, students may use these credits to complete a minor, enroll in a practicum or internship, or study abroad.
















* Students may take C110/111 Computer Science I & Lab in place of CS106.  
Please Note:  Certification to teach at the secondary level may require students to have an overload one or two semesters. To avoid an overload of courses, student may choose to take courses during the summer with the approval of the department chair. Students who are required to take skillbuilding courses or who withdraw from courses may need more time to satisfy all requirements. 
It is the responsibility of the student to complete all major and university requirements. Please refer to the university catalog for additional information regarding this major. Course title and content is subject to change. Not all courses are offered each semester or year. Please consult with your major advisor for the most current information.
Students enrolled in the Lasallian Honors Program should consult the program director for the appropriate sequence of courses.
(From the 201315 Catalog)
The following courses are required for graduation.
A. Calculus Core
All of the following:
(Either M148 and M149 or M151)
M148  Calculus with Precalculus I (4 credits)
This course, followed by M149, provides a twosemester sequence that covers the material of a traditional Calculus I course along with builtin coverage of precalculus topics. Topics in M148 include: solving equations, functions, classes of functions (polynomial, rational, algebraic, exponential, logarithmic), right triangle trigonometry, angle measure, limits and continuity, derivatives, rules for derivatives. Credit is not granted for this course and M151 or courses equivalent to college algebra and college trigonometry.
Prerequisite: mathematics competency satisfied.
M149  Calculus with Precalculus II (4 credits)
This course completes the twosemester sequence that begins with M148, and together with M148 provides a twosemester sequence that covers the material of a traditional Calculus I course along with builtin coverage of precalculus topics. Topics in M149 include: trigonometric and inverse trigonometric functions, rules for derivatives, applications of derivatives, and definite and indefinite integrals. Credit is not granted for this course and M151.
Prerequisite: M148.
This course provides an introduction to the differential and integral calculus. Topics include: the concepts of function, limit, continuity, derivative, definite and indefinite integrals, and an introduction to transcendental functions. Credit is not granted for this course and M148 and M149.
Prerequisites: departmental placement or courses equivalent to college algebra and college trigonometry.
M152  Calculus II (4 credits)
This course is a continuation of M151. Some of the topics of M151 are revisited at a higher mathematical level. Topics include: applications of the definite integral, techniques of integration, improper integrals, introduction to differential equations, numerical methods for integration and approximation, curves in the plane given parametrically, polar coordinates, and vectors in 2space and 3space.
Prerequisite: Minimum grade of C in either M149 or M151 or departmental placement.
M251  Calculus III (4 credits)
This course continues the development of Calculus from M151 and M152. Topics include: sequences and series, and differentiation and integration of vectorvalued functions and functions of several variables.
Offered fall semester. Prerequisite: Minimum grade of C in M152.
B. Mathematics Core
All of the following:
M252  Linear Algebra (4 credits)
This course provides an introduction to techniques and applications of linear algebra. Topics include: systems of linear equations, matrices, determinants, Euclidean nspace, real vector spaces, basis and dimension, linear transformations, inner products, and eigenvalues and eigenvectors.
Offered spring semester. Prerequisite: Minimum grade of C in M152.
M301  Foundations of Advanced Mathematics (2 credits)
This course looks at topics central to further study in mathematics. Topics include symbolic logic, especially as it applies to mathematical proof; methods of mathematical proof such as direct proof, indirect proof, proof by induction; use and meaning of mathematical quantifies and predicates; sets; relations; equivalence relations and partitions; order relations; functions and their properties; and complex numbers. A junior assessment test is administered as part of this course.
Offered fall semester. Prerequisite: M251 (may be concurrent).
M332  Probability (2 credits)
This calculusbased course is designed to provide mathematics majors and minors with an introduction to the mathematical underpinnings of statistics. Topics include: probability axioms, probability, Bayesﾒ Theorem, random variables, discrete and continuous probability distributions, and expected value.
Offered spring semester. Prerequisite: M152.
M401  Abstract Algebra (3 credits)
This course provides an introduction to algebraic structures. Topics include: groups, subgroups, quotient groups, group homomorphisms, rings, ideals, and fields.
Offered in alternate spring semesters. Prerequisites: M251, M252, and M301.
M411  Introduction to Analysis (3 credits)
This course provides a rigorous treatment of topics in calculus. Topics include: sequences, functions, limits, continuity, derivatives, and integration.
Offered in alternate spring semesters. Prerequisites: M251, M252, and M301.
M491  Senior Seminar (2 credits)
This course consists of student presentations from mathematics, mathematical modeling, mathematics education, or statistics. Each student chooses a topic in consultation with the instructor, do appropriate background reading, and prepare an oral presentation and written paper on the topic. A senior assessment test is administered as part of this course.
Offered spring semester. Prerequisite: senior mathematics major.
ST232  Introduction to Statistics (2 credits)
This course is designed to provide the basic ideas and techniques of statistics. Topics include: descriptive and inferential statistics, an intuitive introduction to probability, estimation, hypothesis testing, chisquare tests, regression and correlation. This course makes significant use of appropriate technology. Topics in this course are treated at a higher mathematical level than they are treated in ST132. Credit is not granted for this course and any of the following: BU215, B392 or ST132.
Offered fall semester. Prerequisite: departmental placement or minimum C grade in M148.
Prerequisites:
M115 College Algebra
C. Both of the following:
M321  Modern Geometry (3 credits)
This course is required for the Mathematics Education major. The course is designed to be an introduction to the foundations of geometry. Topics include: Euclidean geometry, nonEuclidean geometry, projective geometry, and geometric transformations.
Offered in alternate spring semesters. Prerequisite: M152.
M361  Operations Research (3 credits)
This course is required for the mathematics education major, providing an introduction to techniques and applications of operations research. Topics include: linear programming, game theory, queuing theory, Markovian decision processes, and decision theory.
Offered in alternate spring semesters. Prerequisites: M252 and M332.
D. Two of the following courses: or one of the following courses and one course in another field using mathematics with the approval of the major advisor and the department chair.
M310  Combinatorics and Graph Theory (3 credits)
This course provides an introduction to combinatorial and graph theoretical techniques in mathematics. It is also designed for students in computer science. Topics include: sets, functions, combinatorial techniques, graph theory, searching algorithms, and trees.
Prerequisites: CS106 or CS110/111, and M152.
M315  Number Theory (3 credits)
This course provides an introduction to elementary number theory. Topics include: divisibility, prime and composite numbers, congruences, arithmetical functions, primality testing, factorization techniques, and applications to cryptography.
Prerequisite: M152.
M341  Differential Equations with Applications (3 credits)
This course provides an introduction to the theory, methods, and applications of ordinary differential equations. Topics include: first order differential equations, linear differential equations with constant coefficients, and systems of differential equations.
Prerequisites: M251 and M252.
M342  Numerical Analysis (3 credits)
This course provides an introduction to the theory and methods of numerical analysis. Topics include: numerical methods for solving linear and nonlinear equations, polynomial approximation of functions, numerical integration and differentiation, numerical approximation to solutions of differential equations, direct and iterative methods for solving systems of equations.
Prerequisites: either CS106 or CS110/111, and M251, M252.
M344  Applied Mathematics (3 credits)
This course serves physics majors as well as those mathematics majors whose area of interest is analysis. Topics include: Fourier series, the complex numbers, analytic functions, and derivatives and integrals of complex functions. Other topics may include Laurent series and residues, partial differential equations and boundary value problems.
Prerequisites: M251 and M252.
M348  Complex Analysis (3 credits)
This course provides an introduction to the theory of functions of one complex variable. Topics include: the complex numbers, the complex derivative, analytic functions, power series, complex integration, Cauchyﾒs Theorem and Cauchyﾒs Integral Formula, Laurent series, and residues and poles.
Prerequisite: M251.
M356  Introduction to Scientific Computing (3 credits)
A course designed to provide undergraduates students with the basic computational tools and techniques needed for their study in science and mathematics. Students learn by doing projects that solve problems in physical sciences and mathematics using symbolic and compiled languages with visualization. By use of the Sage problemsolving environment and the Python programming language, the students learn programming and numerical analysis in parallel with scientific problem solving.
Also offered as CS356 and P356. Prerequisites: CS106, M251, M252, and ST232.
M380389  Special Topics (3 credits)
Special topics in mathematics may be offered depending on student interest.
M496/497  Mathematics Internship (117 credits)
This opportunity provides the student with experience in mathematical research or applications. The internship must be approved by the department and, depending on the nature of the internship, may be counted towards the major. Students generally are expected to give a presentation following the internship.
ST350359  Special Topics (3 credits)
Selected topics in statistics may be offered depending on student interest.
ST371  Applied Regression Analysis (3 credits)
This course provides students with an introduction to linear and nonlinear models in statistics. Topics include: linear regression, multiple regression, one, two, and higherway analysis of variance, and popular experimental designs. Realworld problems are analyzed using appropriate technology.
Prerequisites: M251, M332, and ST232.
ST373  Design of Experiments (3 credits)
This course provides an introduction to the principles of the design of experiments from a statistical perspective. Topics include: Analysis of variance, covariance, randomization, completely randomized, randomized block, Latinsquare, factorial, response surface methods and other designs.
Prerequisites: M152 and ST232.
ST431  Mathematical Statistics I (3 credits)
This course provides a mathematical treatment of probability and statistics. Topics include: several descriptions of the concept of probability, univariate and bivariate probability distributions, joint and marginal probability distributions, covariance, hypothesis testing, estimation, data analysis, and sampling distributions.
Prerequisites: M332 (may be concurrent) and ST232.
ST496/497  Statistics Internship (117 credits)
This opportunity provides the student with experience and training in statistical techniques. The internship must be approved by the department and, depending on the nature of the internship, may be counted towards the major. Students usually are expected to give a presentation following the experience.
E. Either CS106 or CS110 and CS111
CS106  Introduction to Programming for Sciences (3 credits)
This course teaches introductory programming within a problem solving framework applicable to the sciences. The course emphasizes technical programming, introductory data storage techniques, and the processing of scientific data. There is an emphasis on designing and writing correct code using an easy to learn scientific programming language such as Python. Advanced excel spreadsheet concepts will be taught and utilized during the programming process.
Prerequisite: mathematics competency.
CS110  Computer Science I: Introduction to Programming (3 credits)
This course introduces students to the practice of software development. Students learn the fundamentals of programming, algorithm development, and basic design principles.
Offered spring semester. Prerequisite: CS101; concurrent with CS111.
CS111  Computer Science I Laboratory (1 credit)
The laboratory course complements CS110 by using programming exercises to reinforce concepts and practices covered in CS110 lectures.
Offered spring semester. Prerequisite: CS101; concurrent with CS110.
F. Required education course work