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Degrees / Courses

 
Degrees Courses Online Courses  
 

Degrees

Major Requirements
Thirty-two (32) semester hours, including MS121, MS122, MS231, MS232, MS321, and an additional 13 semester hours to be selected from those courses having MS121 as a prerequisite. At least 16 semester hours of mathematics must be taken at Aquinas and the successful completion of
the capstone requirement detailed below. The Department of Mathematics requires a two-semester immersion into mathematics most useful for their majors. Although a major may choose any of the three course pairing options; the three apply to specific directions after graduation. For prospective teachers, the recommended capstone pair is Math History MS351 and Secondary Methods MS375. For finance, actuarial science, biostatistics and other such applications, the capstone recommendation is MS493 and MS494 Probability and Statistics. For graduate work or any other focus in pure mathematics, the capstone pair recommended is MS401 Real Analysis and MS321 Abstract Algebra.
 
Minor Requirements
Twenty-four (24) semester hours including MS121 and MS122. Of the remaining 16 hours, a minimum of 12 hours of core courses are to be
selected from those courses having MS121 as a prerequisite. MS252 may also be included in the core courses. At least 12 semester hours of
mathematics must be taken at Aquinas. Each mathematics major or minor requires departmental approval. To qualify for either a major or a minor in mathematics a student must have, at graduation time, a cumulative G.P.A. of C+ (2.3) or higher in those courses which he/she is using to fulfill the major or minor requirements. No course with a grade below a Cā€“ will count toward the mathematics major or minor. Upper-division courses (300ā€“400 level) generally are offered on alternate years.
 
Teaching Mathematics
Secondary Level (6 - 12 certification)
Students seeking a secondary teaching major or minor must fulfill all requirements for the mathematics major/minor described above. In addition to the other requirements for the major/minor, all students earning secondary mathematics teacher certification must include one department approved course in Geometry, one department approved course or course sequence in Probability and Statistics, one department approved course in Discrete Math, and one department approved course in the History of Mathematics. Additional recommended courses are MS170 and MS321.
 
Elementary Level (K - 8 certification)
Students seeking an elementary teaching major must fulfill all requirements for the mathematics major, described above. Included in the 32 credits required for the math major there must be at least one department approved course or course sequence in Probability and Statistics and one department approved course in the History of Mathematics. In addition to the 32 credits required for the major, candidates must also complete MS260, MS261, and MS271 for certification requirements.
Mathematics Minor for Elementary Certification requires 24 credit hours, including MS121, MS122, and a minimum of 16 hours selected from MS114, MS252 and those core courses requiring MS121 or higher as a prerequisite. Included in the 24 credits must be at least one department approved course or course sequence in Probability and Statistics, and one department approved course in the History of Mathematics. Certification requirements of MS260, MS261, and MS271 must also be met.
 
Since the above are State of Michigan requirements, they apply to all students (graduates and undergraduates) seeking mathematics teacher certification. Major/minor programs require departmental approval.
 
Math/CIS Minor
Math/Computer Science Minor Requirements: 24 hours including MS121, MS170, CS180 and MS240, and a one-or two-hour research project (399) that is supervised by a faculty member from the student's major field and uses the computer for modeling, data gathering, data analysis, or internet security. Remaining courses chosen from a list of approved courses, currently including MS122, MS232, MS252, MS309, MS310, MS332, CS170, CS182, CS242, and CS332. At least two courses must be taken through CIS department.
 
Credit-No Credit
Only courses which are not to be applied toward a mathematics major or minor, or to fulfill requirements in other content areas, may be taken on a Credit-No Credit basis.
 

Courses

MS107 Elementary Algebra (3)
Real numbers, algebraic expressions, linear, rational and quadratic equations, graphing, factoring. Prerequisite: Designed for students having no more than two years of college preparatory mathematics.
 
MS110 Mathematics for Liberal Arts (3) MS
Mathematical ideas for understanding life in our culture; topics include probability, logical thinking, and problem solving with minimal use of algebra. Prerequisite: Two years of college-preparatory mathematics or MS107.
 
MS111 Intermediate Algebra and Trigonometry (4) MS
Linear and quadratic equations, inequalities and functions; exponential and logarithmic functions; exponents, radicals; polynomial and rational functions. Introduction to trigonometric functions and relationships. Prerequisite: Two years of college-preparatory mathematics or MS107.
 
MS114 College Algebra and Trigonometry (4) MS
Linear and quadratic functions; equations and inequalities; transformations; systems of linear equations and inequalities; polynomial, rational, exponential, logarithmic and trigonometric functions, and graphing; conic sections. Prerequisite: Three years of college-preparatory math or MS111.
 
MS117 Finite Mathematics (3)
Functions: linear, quadratic, polynomial, rational, exponential, and logarithmic; matrix algebra; linear programming and finance as applied to business problems.
Prerequisite: Three years college-preparatory math or MS111.
 
MS118 Business Analysis (3) QR
Short course of differential and integral calculus for applications in business, sustainable business and economics and an emphasis on optimization. Prerequisite: Three and one-half years of college- preparatory math or MS114.
 
MS121, 122 Calculus with Analytic Geometry (4,4) MS
Functions, limits, continuity, derivatives, and integrals with applications; inverse functions; sequences and series; conic sections; polar coordinates; parametric equations. Prerequisites: Three and one-half years of college-preparatory math, including trigonometry or MS114. (MS121 is a prerequisite for MS122.)
 
MS151 Elementary Statistics (3) QR
Designed primarily for students who have had no more than two years of high school mathematics or its equivalent. Includes the fundamental concepts of
descriptive and inferential statistics. Prerequisite: MS107
 
MS170 Technology and Mathematics Seminar (1)
Introduces programming and applications of computer algebra systems, modeling programs, calculators, and other mathematical software and hardware. This
course prepares prospective teachers, minors and majors for higher courses and their own work as educators. Prerequisite: MS121, can be taken concurrently.
 
MS211 Introduction to Scientific Programming with FORTRAN (3)
A structured programming course designed to teach students the fundamentals of FORTRAN, a primary computer language used in scientific, mathematical, and engineering applications. Topics covered include problem-solving techniques, internal representation of data, and file manipulation. Prerequisites: Three years of college-preparatory math or MS114 or department approval.
 
MS231 Multivariate Calculus (4) QR
Vector and solid geometry, vector-valued functions, calculus of curves in space, functions of several variables, partial differentiation, multiple integration, and
vector analysis. Prerequisite: MS122.
 
MS232 Linear Algebra (3)
Systems of equations, matrices, determinants, vector spaces, linear transformation, eigenvalues, eigenvectors, and canonical forms. Prerequisite: MS122.
 
MS240 Discrete Mathematics (3)
Develop basic techniques and modes of reasoning of combinatorial problem solving; describe and analyze the algebraic structures of certain set-relation systems; illustrate and analyze the wide variety of applications of discrete mathematics. The topics to be covered include mathematical induction, set theory, relations and functions, combinatorics, probability, graph theory, and mathematical logic. Prerequisite: MS121 or department approval.
 
MS241 Differential Equations (3)
Study of the classification and solutions of ordinary differential equations with applications. Prerequisite: MS231.
 
MS252 Statistics (3)
Designed for students who have had at least three years of high-school mathematics or its equivalent. Topics to be covered include frequency distributions,
variability, probability, sampling, estimation, testing, hypotheses, analysis of variance, regression and correlation analysis, and nonparametric tests. (Course
counts as 3 credits toward a minor, but only 1 credit toward a major.) Prerequisite: MS114.
 
MS260 Mathematics for Elementary and Middle-School Teachers I (3)
Required for elementary certification. Topics appropriate for grades K-8 include: rational numbers, patterns and variables, measurement, geometry, logic, and graphing. Emphasis is on constructing understanding through experience: exploring, extrapolating, and explaining concepts and relationships. Problem solving, both in groups and individually, is a major theme. Tutoring and field experiences required. Prerequisites: EN201; cumulative grade point average of 2.5 and a grade of C in MS111 or equivalent.
 
MS261 Mathematics for Elementary and Middle-School Teachers II (3)
Required for elementary certification. Topics appropriate for grades K-8 include: elementary algebraic preparation including linear, quadratic and exponential, probability and statistics. Emphasis is on constructing understanding through experience: exploring, extrapolating, and explaining concepts and relationships. Problem solving, both in groups and individually, is a major theme. Tutoring and field experiences required. Prerequisites: EN201; cumulative grade point average of 2.5 and a minimum grade of C in MS260
 
MS271 Mathematics Methods for Elementary and Middle-School Teachers (3)
Required for elementary certification. Course expands on the content from MS260, 261, examines ways children learn and fail to learn mathematics, and emphasizes strategies for teaching and designing lessons. New content focuses on concepts and operations of whole numbers, number theory, number patterns, and measurement. Tutoring and field experiences required. Prerequisite: EN201, MS260 , MS261; cumulative grade point average of 2.5 and a grade of C MS111 or equivalent.
 
MS309 Theory of Numbers (3)
Divisibility, congruences, quadratic reciprocity, arithmetic functions, multiplicative number theory, Riemann's zeta function. Prerequisite: MS122.
 
MS310 Modern Cryptography (3)
Encoding (RSA, EIGamal and elliptic curves) and decoding methods (Meller-Rabin, Dixon and Pollard) form 1974 to the present. Electronic signatures and hash functions. We will study the math behind these ideas and write programs which perform the encoding and decoding. Prerequisite: MS309.
 
MS/PC316 Applied Mathematics for the Physical Sciences (4)
An introduction to topics in applied mathematics not covered in a traditional mathematics curriculum. Topis include Complex Numbers, Fourier Series, Fourier Analysis, Partial Differentiation, and Laplace Transforms. Prerequisite: MS122. Cross-listed as MS316.
 
MS321 Abstract Algebra (4) SC (Senior Capstone with MS 401)
Sets, functions, equivalence relations, integers, mathematical induction, modular systems, permutations, groups, rings, fields, isomorphisms, and homomorphisms.
Prerequisite: MS122, MS232 (MS240 recommended).
 
MS332 Introduction to Numerical Analysis (3)
Numerical methods involving polynomial evaluation, series approximations, numerical integration, interpolation of linear and differential equations, least squares, and minimax approximations.
Prerequisite: MS231, MS232 and CS180 or department approval.
 
MS351 History of Mathematics (3) SC (Senior Capstone with MS 375)
Survey of the development of mathematics from ancient to modern times. Prerequisite: MS122.
 
MS375 Methods of Teaching Secondary Mathematics (3) SC (Senior Capstone with MS 351)
Provides a detailed examination of the pedagogy for teaching the mathematical content and process strands of secondary mathematics curricula and of appropriate instructional and assessment strategies. Tutoring component required. Prerequisite: EN201 (can be taken concurrently with MS375); MS122; cumulative grade point average of 2.5.
 
MS397 Field Experience in Mathematics (Variable)
One or two semester hours of internship or experience in a field directly related to mathematics, negotiated between Mathematics Department and student. Prerequisite: Approval of the chairperson.
 
MS398 Readings in Mathematics (Variable)
Individually-negotiated program of readings on selected topic established by contract between instructor and student. Contracts filed with Registrar. Prerequisite: Department approval.
 
MS399 Independent Project (Variable)
Individually-negotiated project of defined nature established by contract between instructor and student. Contracts filed with Registrar. Prerequisite: Department approval.
 
MS401 Introductory Real Analysis (3) SC (Senior Capstone with MS 321)
Properties of real numbers, Cauchy sequences, series, limits, continuity, differentiation, Riemann integral, sequences, and series of functions. Prerequisite: MS231.
 
MS433 Topics in Geometry (3)
Topics selected from affine, Euclidean, non-Euclidean, and projective geometry. Prerequisite: MS122.
 
MS491, 492 Advanced Topics in Mathematics (Variable)
Prerequisite: MS231 or instructor approval.
 
MS493 Probability (3) SC (Senior Capstone with MS 494)
Probability theory and distributions, large and small sample theory. Prerequisite: MS122 or department approval.
 
MS 494 Mathematical Statistics (3) SC (Senior Capstone with MS 493)
Tests of hypotheses, point and interval estimation, non-parametric statistics, regression and correlation, analysis of variance.MS493 is a prerequisite for\break MS494.)
 
MS499A, B, C, D Mathematics Seminar (1 each)
Topics selected to broaden the students’ mathematical background. Prerequisites: MS122 and junior status. Not more than two semester hours may be applied to the major.