Mathematics Catalog 05-07

The Department of Mathematics and Computer Science offers the following math programs:

Majors

Mathematics 
Mathematics Teaching (early adolescent to adolescent (formerly grades 6-12) and adolescent (formerly grades 9-12))

Minors

Mathematics
Mathematics Teaching (early adolescent to adolescent (formerly grades 6-12) and adolescent (formerly grades 9-12))
Elementary/Middle School Mathematics Teaching (early/middle childhood (formerly grades 1-6) and early/middle childhood to early adolescent (formerly grades 1-9))

Mathematics

The mathematics major is designed to meet the needs of students planning to enter a wide variety of vocations. The major has sufficient flexibility to prepare a student for graduate study in mathematics and/or to enter into a career in teaching, statistics, computer science, actuarial science, business, economics or engineering. In addition to a thorough preparation in specific areas of mathematics, the student who majors in mathematics will develop a habit of accuracy and logical thought processes, acquire an appreciation of the aesthetic qualities and historical development of mathematics, and gain an appreciation and understanding of concepts and techniques in mathematics that are applicable to other areas of scientific endeavor. Any student who completes a mathematics major should be well on the way toward entering one of the above-mentioned vocations, all of which will be in high demand.

Mathematics Major

A minimum of 41 credits in mathematics, including:

1. Required courses:

            MATH 121: Statistics
            MATH 231: Calculus I
            MATH 232: Calculus II
            MATH 233: Calculus III
            MATH 301: Proof and Problem Solving
            MATH 341: Linear Algebra
            MATH 485: Mathematics Seminar

2. One of the following:

            CS 180: Introduction to Computer Science,
            CS 201: Programming in C++,
            Demonstrated proficiency in a computer-based computer algebra system.

3. At least five additional mathematics courses with at least 18 credits from the following list, chosen with the consent of the student's academic advisor, to include at least one from each of the three pairings:

            MATH 331: Differential Equations
            MATH 371: Topics in Applied Mathematics
            MATH 471: Topics in Pure Mathematics

    Analysis Pairing:

MATH 431: Real Analysis
MATH 432: Complex Analysis

    Algebra Pairing:

            MATH 441: Abstract Algebra
            MATH 442: Number Theory

    Geometry Pairing:

            MATH 461: Geometry
            MATH 462: Topology

4.. A minimum GPA of 2.5 in the above mathematics courses.

5. Satisfactory Completion of the Major Field Achievement Test in Mathematics.

Mathematics Teaching Major

A minimum of 49 credits in mathematics including:

1. Required Courses:

            MATH 121: Statistics
            MATH 231: Calculus I
            MATH 232: Calculus II
            MATH 233: Calculus III
            MATH 301: Proof and Problem Solving
            MATH 341: Linear Algebra
            MATH 431: Real Analysis
            MATH 441: Abstract Algebra I
            MATH 442: Abstract Algebra II                                                
            MATH 451: Explorations of Middle/Secondary School Mathematics
            MATH 459: Middle/Secondary Math Methods (crosslisted with ED 459M)
            MATH 461: Geometry
            MATH 485: Mathematics Seminar.

2. One of the following:

            CS 180: Introduction to Computer Science,
            CS 201: Programming in C++,
            Demonstrated proficiency in a computer-based computer algebra system.

3. A minimum GPA of 2.5 in the above mathematics courses.

4. Completion of the general education requirements, the professional core prerequisites, and the professional education requirements for the licensing sequence in either middle/secondary or secondary education. Admission to teacher education is recommended as early as possible.

5.  Satisfactory Completion of the Major Field Achievement Test in Mathematics.

Mathematics Minor

A minimum of 24 credits in mathematics including:

1. Required Courses:

            MATH 121: Statistics
            MATH 231: Calculus I
            MATH 232: Calculus II
            MATH 301: Proof and Problem Solving
            MATH 341: Linear Algebra
            MATH 485: Mathematics Seminar

2. At least two of the following with at least 6 credits:

            MATH 233: Calculus III
            MATH 331: Differential Equations
            MATH 371: Topics in Applied Mathematics
            MATH 431: Real Analysis
            MATH 432: Complex Analysis
            MATH 441: Abstract Algebra I
            MATH 442: Abstract Algebra II
            MATH 461: Geometry
            MATH 462: Topology
            MATH 471: Topics in Pure Mathematics

3. A minimum GPA of 2.5 in the above mathematics courses.

4. Satisfactory Completion of the Major Field Achievement Test in Mathematics.

Mathematics Teaching Minor

A minimum of 29 credits in mathematics including:

1. A teaching major in some field for secondary or middle/secondary education.

2. Required Courses:

            MATH 121: Statistics
            MATH 231: Calculus I
            MATH 232: Calculus II
            MATH 301: Proof and Problem Solving
            MATH 341: Linear Algebra
            MATH 451: Explorations of Middle/Secondary School Mathematics
            MATH 459: Middle/Secondary Math Methods (crosslisted with ED 459M)
            MATH 461: Geometry
            MATH 485: Mathematics Seminar

3. A minimum GPA of 2.5 in the above mathematics courses.

4. Completion of the general education requirements, the professional core prerequisites, and the professional education requirements for the licensing sequence in either middle/secondary or secondary education (see EDUCATION). Admission to teacher education is recommended as early as possible.

5. Satisfactory Completion of the Major Field Achievement Test in Mathematics.  

Elementary/ Middle School Mathematics Teaching Minor

A minimum of 21 credits in mathematics including:

1. A major in elementary or elementary/middle school education (at the early and/or middle childhood licensure level).

2. Required Courses:

MATH 101: Introduction to Problem Solving
MATH 102: Arithmetic Structures
MATH 103: Geometric Structures
either MATH 111: College Algebra or Math 131 Mathematical Modeling 
MATH 112: College Algebra and Trigonometry 
MATH 121: Statistics
MATH 231: Calculus I

ED 428: Elementary/Middle Mathematics Methods 
MATH 451: Explorations of Middle/Secondary School Mathematics

 3. At least two out of the following courses, in consultation with the minor advisor:

MATH 122: Finite Mathematics
MATH 232: Calculus II
 

4. A minimum GPA of 2.5 in the above mathematics courses.

5. Completion of the general education requirements, the professional core prerequisites, and the professional education requirements for the licensing sequence in either middle/secondary or secondary education (see EDUCATION). Admission to teacher education is recommended as early as possible.

Assessment

  The Department of Mathematics and Computer Science has identified five goals for the students majoring in math and math education:

1. Core mathematics. Students should demonstrate a broad understanding of core mathematics as defined by the requirements for the major and the department’s course goals. These goals should include the interplay of mathematics with other disciplines and the history of mathematics.
    

2. Problem-solving. Students should demonstrate competency in problem-solving. This includes the ability to generate special cases, recognize patterns, formulate and test conjectures, reject incorrect solutions, use mathematical tools developed in coursework, and reflect appropriately on the solution.  
   

3. Proof. Students should demonstrate the ability to critically examine mathematical arguments and produce proofs that are both mathematically and stylistically correct.  
   

4. Communication. Students should be able to communicate mathematics effectively in oral and written form using formal definitions, appropriate mathematical terminology and convenient symbolism.  
   

5. Technology.  Students should be able to use appropriate technology as a tool in understanding mathematics, solving problems, and presenting solutions.

  The Math Faculty assesses how well students are meeting the goals through: final exams on departmental course goals, projects, oral presentations, and a standardized Major Field Achievement Test (MFAT). Students participate in assessment through regular course work and by taking the MFAT shortly before graduation.

Student Employment  

The academic experience for students in mathematics is enriched when they have the opportunity to be employed by the Department in a capacity related to the major such as grading papers or tutoring. The Department will attempt to find relevant employment for qualified students majoring or minoring in mathematics. Students are encouraged to take advantage of this opportunity and should contact the Department Chair for more information.

Internships and Careers in Mathematics

There are a large number of careers open to students majoring in mathematics. Highly qualified students should consider graduate school in an advanced mathematical or technical field. Other students will move into the work force directly from college. Many students choose to become teachers at the middle or secondary level. The student majoring in mathematics should talk to her/his advisor early (in the sophomore or junior year) to explore internships and career opportunities. Members of the department will work with the student and Edgewood's Career Services office to help the student successfully chart a path beyond graduation.

Suggested Mathematics Course Sequence for Math and Math Teaching Majors

There are two suggested sequences of mathematics courses at or above the calculus level for majors, depending upon whether you start the calculus sequence in the fall of an even or odd year. Both sequences can be completed in three years, starting from when you begin calculus. So if you start the calculus sequence in your first year, it is possible to complete the math requirements by the end of your third year or to spread out some of your coursework, keeping the rotation of math courses in mind. If you start the calculus sequence in your second year or you decide to take Problem Solving & Proof in the spring of your second year, it is possible to complete the math requirements by the end of your fourth year.

Even Year/Odd Year

Odd Year/Even Year 

The Foundations of Communication Math Requirement

The math requirement may be satisfied by completing MATH 101, or any college-level algebra, pre-calculus or calculus course with a passing grade or demonstrated proficiency. To further clarify this point, the following courses meet the Foundations of Communications math requirement: MATH 101, MATH 111, MATH 112, MATH 122,  MATH 131, MATH 232 and MATH 233. The following courses do not satisfy the Foundations of Communications math requirement: MATH 98, MATH 99, Intermediate Algebra, MATH 102, MATH 103 and  MATH 121. Note that Elementary Education majors need to take MATH 101 or demonstrate proficiency in that course as part of their major even if placed in MATH 112, MATH 231 or higher.

Policies

A student must have a cumulative grade point average of 2.5 or above in major/minor level mathematics courses in order to major or minor in mathematics or mathematics teaching. 

A minimum of three courses in the math and math teaching majors and minors at or above the 300 level or two courses in the minor approved by the Department must be taken in the Department of Mathematics and Computer Science at Edgewood College. 

Students intending to major or minor in mathematics or mathematics teaching should take MATH 301 as soon after MATH 231 as possible since it is a prerequisite or highly recommended for most of the mathematics courses at the 300 and 400 levels.

Courses in mathematics may not be audited. 

Courses in the department may be taken Pass/Fail only with the consent of both the instructor and the MCS Department Chairperson. 

No student may take any mathematics course Pass/Fail if it is to be used to satisfy any requirement the student has for a major or minor from any department in the College. 

Any course requirement of the math and math teaching majors and minors, other than the minimum residency requirement, may be satisfied through examination. 

All mathematics courses at or above the 200 level will include a significant historical perspective. 

Students in a math teaching major should not plan to take upper division mathematics courses during the semester in which they are student teaching. 

The general education computer proficiency requirement of mathematics and mathematics teaching majors is fulfilled by taking either CS 180 or CS 201 or demonstrated proficiency in a computer-based computer algebra system.

Courses Offered

Courses that are usually taught in the Fall semester are followed by (F); those usually taught in Spring are followed by (S); those usually taught in the summer are followed by (SS). Courses offered on a two-year rotation have an “o” for odd year or an “e” for even year preceding the “F” or “S”. Contact the specific department in instances where this information is not provided.

98 Mathematical Connections 3 cr

A course in quantitative reasoning that examines the arithmetic of real numbers, geometry, measurement, and algebra using application and problem solving techniques. An emphasis is placed on exploring these mathematical concepts within the context of global issues. No Prerequisite. (F/S)

99 Math Workshop  2 cr

Continuation of Mathematical Connections. Must be taken the semester after MATH 98. (Prerequisite: Consent of instructor) (F/S)

101  Introduction to Problem Solving 3 cr

An introduction to problem solving and mathematical thinking; the focus of this course is on the process of mathematics rather than specific techniques or content. Students will engage in mathematical problem solving in a variety of contexts and learn a number of broadly applicable ways of approaching new problems. This course satisfies the College general education requirement in math. (Prerequisite: satisfactory score on placement examination or passing grade in MATH 98) (F/S/SS)

102 Arithmetic Structures 3 cr

This course focuses on the arithmetic and algebraic content of Pre-K--8 mathematics and appropriate teaching methods.  Instruction will be guided by the NCTM Principles and Standards for School Mathematics and the Wisconsin Model Academic Standards for Mathematics.  Emphasis is on problem solving, critical thinking, and communication.  This course does NOT satisfy the college General Education requirement in math.   (Prerequisite: MATH 101 with a grade of "C" or above) (F/S/SS)  

103  Geometric Structures 3 cr

This course focuses on the geometric and measurement content of Pre-K--8 mathematics and appropriate teaching methods.  Instruction will be guided by the NCTM Principles and Standards for School Mathematics and the Wisconsin Model Academic Standards for Mathematics.   Emphasis is on problem solving, critical thinking, and communication. This course does NOT satisfy the college General Education requirement in math. (Prerequisite: MATH 102 with a grade of "C" or above) (F/S)

111 College Algebra 3 cr

Course topics include basic algebraic skills, equations and systems of equations, inequalities, functions and their properties, and applications.  The emphases of the course will be on using linear, quadratic, and exponential functions to model real-world phenomena and on drawing conclusions about the world from those models.  This course satisfies the college General Education requirement in mathematics. (Prerequisite: satisfactory score on placement examination or passing grade in MATH 98) (F/S/SS)

112 College Algebra and Trigonometry 4 cr

Course topics include basic algebraic skills, equations and systems of equations, inequalities, functions and their properties, and applications.  The emphases of the course will be on using linear, quadratic, exponential functions, and trigonometric to model real-world phenomena and on drawing conclusions about the world from those models.  This course satisfies the college General Education requirement in mathematics.  (Prerequisite: MATH 111 or placement) (F/S)

121 Statistics 3 cr

Course topics include descriptive and inferential statistics with the emphasis on drawing meaningful conclusions from sets of data. Topics include measures of central tendency and dispersion, the normal distribution, z-tests, t-tests, linear regression, analysis of variance, Chi-Square tests, and other topics as time permits. This course does NOT satisfy the College General Education requirement in math. (Prerequisite: MATH 101 or 111, or placement) (F/S/SS)

122 Finite Mathematics 3 cr

An introduction to finite mathematics; course topics including linear systems, linear programming, mathematics of finance, probability, and other related topics. This course is designed primarily for business majors. This course satisfies the College General Education requirement in math. (Prerequisite: MATH 111 or placement) (F/S/SS)

131  Mathematical Modeling 3 cr

A mathematical modeling approach to understanding the relationships between data, tables, graphs and functions. Topics include linear, quadratic, exponential, logarithmic functions; curve fitting; linear and exponential regression. Applications to various disciplines are investigated through the construction and analysis of mathematical models. The course is intended to be equivalent to College Algebra and satisfies the College General Education requirement in math. (Prerequisite: satisfactory score on placement examination or passing grade in MATH 98)

171 Topics of Mathematics 1-3 cr

This course is offered in response to student needs and interests.  Topics vary. This course does NOT satisfy the College General Education requirement in math unless explicitly stating so in its course description.

231 Calculus I 4 cr

An introduction to differential and integral calculus; course topics include derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus. This course emphasizes the mastery of key concepts and their applications. This course satisfies the College General Education requirement in math. (Prerequisite: MATH 112, high school calculus or placement) (F/S)

232 Calculus II 4 cr

This course is a continuation of differential and integral calculus. Topics include integration techniques, improper integrals, applications, differential equations, Taylor polynomials, and infinite series. This course emphasizes the mastery of key concepts and their applications. This course satisfies the College General Education requirement in math. (Prerequisite: MATH 231 with a grade of “C” or above) (S)

233 Calculus III 4 cr

An introduction to multivariable calculus; topics include vectors, curves, partial derivatives, differential forms, gradients, multiple and iterated integrals, Green’s and Stokes’ theorems. This course satisfies the College General Education requirement in math. (Prerequisite: MATH 232 with a grade of “C” or above) (F)

301 Problem Solving and Proof 3 cr

This course is intended as a gateway to upper-level mathematics courses.  The emphasis is on creative problem solving strategies, structures and techniques of proof, as well as effective oral and written communication of mathematical ideas.  It is designed to ease the transition from algebra and calculus to more theoretical courses such as abstract algebra, geometry and real analysis.  (Prerequisite: MATH 231) (S)

331 Differential Equations 3 cr

Theory of ordinary differential equations with an emphasis on problems of the physical world which are modeled well by differential equations; topics include first order equations, second order and higher linear equations, series solutions, a brief introduction to numerical methods and partial differential equations as time permits. (Prerequisite: MATH 232; MATH 233 highly recommended) (oS)

341 Linear Algebra 3 cr

An introduction to linear algebra including matrices, linear transformations, eigenvalues and eigenvectors; linear programming. (MATH 301 highly recommended) (eS)

371 Selected Topics in Applied Mathematics 1-3 cr

This course is offered in response to student needs and interests.  Topics vary within applied mathematics. (MATH 301 highly recommended)

379 Independent Study 1-3 cr

Independent study of selected topics in mathematics developed by the student with the approval and direction of the instructor. (Prerequisite: consent of the instructor)

431 Real Analysis 4 cr

 This course introduces analysis as a tool necessary for a deeper understanding of calculus. With the least upper bound axiom of the real numbers as its starting point, the course carefully develops the foundations necessary to work with limits and prove results from calculus. Topics include sequences, series, power series, derivatives, and integrals. Time permitting the course will explore how the same tools are used in more advanced settings. (Prerequisite: MATH 233; MATH 301 highly recommended) (oS)

432 Complex Analysis 4 cr

This course continues the study of analysis shifting from the real numbers to complex numbers. Topics include functions of a complex variable, Cauchy's theorem, integration by residues, power series, and conformal mappings. (Prerequisite: MATH 233; MATH 301 highly recommended) Alternates with MATH 462. (oF)

441 Abstract Algebra I 4 cr

This introductory course in abstract algebra is focused mainly on number theory, with an introduction to the concepts of groups, rings, and fields.  Number theoretic concepts include divisibility (such as Bezout’s identity, the fundamental theorem), congruences, number-theoretic functions, Euler’s Theorem, linear Diophantine equations, Quadratic Reciprocity, and applications to cryptography.   (MATH 301 highly recommended (oF)

442 Abstract Algebra II 4 cr

This course continues the study of abstract algebra and is focused mainly on groups, with some exploration of rings and fields as time allows.  Group theoretic topics include subgroups, normal subgroups and quotient groups, and some counting principles.  A wide variety of examples will be explored.  (Prerequisite: MATH 441) (eS)

451 Explorations of Middle/Secondary School Mathematics 4 cr

This course focuses on the content of middle and secondary school mathematics and appropriate teaching methods. Instruction will be guided by the NCTM Principles and Standards for School Mathematics and the Wisconsin Model Academic Standards for Mathematics. Emphasis is on problem solving, critical thinking, communication, and issues of technology as they relate to number and operations, the development of algebraic and geometric reasoning, measurement, data analysis and probability in grades 5-12.  Students will investigate and review the content of current mathematics text series, and will observe and interact with learners engaged in studying these topics.  (Math 301 highly recommended) (eF)

459 Teaching of Mathematics in Middle/Secondary Schools 3 cr

This course is designed to provide an integrative study of curriculum and instruction in mathematics for middle/secondary level classrooms including appropriate research and practice in learning theories, curriculum development, teaching methods, instructional materials, evaluation and assessment at the middle/secondary level.  Emphasis will be placed on the NCTM Principles and Standards for School Mathematics and the Wisconsin Model Academic Standards for Mathematics.   (Prerequisite: MATH 451, junior standing, and either admission to Teacher Education Program, or consent of both Department of Education and Department of Mathematics and Computer Science) Cross listed with ED 459M (S)

461 Geometry 4 cr

An introduction to geometry; topics include postulation development of Euclidean and non-Euclidean geometry; introduction of other geometries: projective, finite, vector, and transformational; historical development of geometry. (MATH 301 highly recommended) (eF)

462 Topology 4 cr

This course continues the study of properties of spaces invariant under homomorphisms. Topics include continuity, homeomorphisms, connectedness, compactness, manifolds, the classification of closed, compact surfaces, the Euler characteristic, the fundamental group, and knot theory. (MATH 301 highly recommended) Alternates with MATH 432. (oF)

471 Selected Topics in Pure Mathematics 1-3 cr

This course is offered in response to student needs and interests.  Topics vary within pure mathematics. (MATH 301 highly recommended)

479 Independent Study 1-3 cr

Independent reading and research of selected topics in mathematics developed by the student with the approval and direction of the instructor. (Prerequisite: consent of the instructor)

483 Mathematics Education Seminar 2 cr

Selected topics in mathematics education and related fields. A seminar format which includes presentations by students, faculty, and outside speakers, and class discussion. Because the content varies, this course may be taken more than once. (Prerequisite: sophomore standing and consent of instructor)

485 Mathematics Seminar 2 cr

Selected topics in mathematics and related fields. A seminar format which includes presentations by students, faculty, and outside speakers, and class discussion. Because the content varies, this course may be taken more than once. (Prerequisite: sophomore standing and consent of instructor) (eF)

490, 491 Internship I, II Arr

Work experience related to the major. (Prerequisite: junior or senior status in the major in mathematics; consent of Department)