The Mathematical Sciences (BA) offers two options:

- Mathematical Sciences (BA)/ Pure Mathematics (MS)
- Mathematical Sciences (BA)/Secondary Education Mathematical Sciences (MEd)

Students apply to this program in spring of their junior year; interested students should meet with the Graduate Program Director of the program. Students in this program take a maximum of twelve graduate credit hours as three courses in their senior year; these graduate courses apply toward both undergraduate and graduate Mathematical Sciences requirements.

This combined degree program of the College of Science and Health and the College of Education was collaboratively developed, and is governed and taught by faculty from these units.

Students may apply to the Program during the spring of their junior year. They must enroll in the Junior Year Experiential Learning course, TCH 320, and meet other application criteria; these include completion of at least 16 quarter credit hours at DePaul and a 3.0 GPA. During their senior year, students are required to complete a Program capstone course, TCH 390, and three 400-level courses that count toward both their undergraduate and graduate degrees:

- TCH 401 TEACHING AS A PROFESSION IN SECONDARY SCHOOL
- TCH 413 THE NATURE OF MATHEMATICS
- TCH 423 INQUIRY & APPLICATION IN DEVELOPING SECONDARY MATHEMATICS PEDAGOGY

Math Content Area (grades of C or better required for licensure):

The following Math content area requirements are required. These can be taken as part of the major, liberal studies or open elective requirements:

- One of the following three-course Calculus sequences:
- MAT 150 , MAT 151, MAT 152
- MAT 147 , MAT 148, MAT 149
- MAT 160 , MAT 161, MAT 162
- MAT 170 , MAT 171 and (MAT 149, MAT 152,MAT 162)
- MAT 215 INTRODUCTION TO MATHEMATICAL REASONING

or (MAT 140 DISCRETE MATHEMATICS I AND MAT 141 DISCRETE MATHEMATICS II) - MAT 260 MULTIVARIABLE CALCULUS I
- MAT 261 MULTIVARIABLE CALCULUS II
- MAT 262 LINEAR ALGEBRA
- CSC 212 PROGRAMMING IN JAVA II

or CSC 262 PROGRAMMING IN C++ II - MAT 310 ABSTRACT ALGEBRA I
- MAT 303 THEORY OF NUMBERS

or MAT 311 ABSTRACT ALGEBRA II - MAT 320 GEOMETRY I
- MAT 321 GEOMETRY II

or MAT 335 REAL ANALYSIS I - MAT 351 PROBABILITY AND STATISTICS I

or MAT 348 APPLIED STATISTICAL METHODS - MAT 301 HISTORY OF MATHEMATICS

The Master’s year comprises teacher-preparation coursework that culminates with student teaching during Spring quarter. Upon graduation and the fulfilling of State of Illinois licensure requirements (which may require some additional course work in the student’s major and related fields), students are eligible to be certified licensed to teach Mathematics at the 6th-12th grade levels.

A full description of the Program can be found on the College of Education website in the graduate course catalog. Students interested in the Program should consult with the designated TEACH Program advisor in their home department.

This course is an introduction to the TEACH Program, including the College of Education's conceptual framework and teacher dispositions, and to the professional world of secondary school teaching, including the policy bodies and stakeholders that impact teaching. Within this developing understanding of the larger context of secondary education, students will begin to articulate clearly professional identities and the behaviors inherent in those identities, including their impact on student learning. Drawing on previous coursework and their growing understanding of differences in individual, ethnic, and cultural group attitudes, values, and needs, students also will learn to recognize the complexities of teaching and learning in a pluralistic society. Ultimately, students will be committed to teaching as a responsible professional who acts in an ethical and collegial fashion. 25 Level 2 field experience required. Offered during Fall term only.

This course builds on students' mathematics understanding by emphasizing the universality of mathematics as a cultural endeavor. In it, students will explore the historical trends in mathematic and how those trends have been taught. Students will understand that, mathematics, at its core, is deductive; however, it also requires intuition. Thus, the course examines the interaction among intuition, experimentation, conjecture, abstraction, and deductive reasoning not only in the classroom but also in the everyday use of mathematics. It also examines the interplay between concrete problem-solving and generalization. Offered during Winter term only.

This course builds on TCH 413 by introducing students to inquiry methods to understand the teaching and learning of mathematics. Students will explore how mathematics has been and is taught by examining major paradigm shifts in mathematics education and the impact those paradigms and shifts have on pedagogical content knowledge, or knowledge of how to teach disciplinary content. Students will use case study methods to look at instructional practices and begin to articulate their own mathematics teaching pedagogy. With the completion of this course, students will have a deeper understanding of mathematical literacy and the barriers to understanding and teaching mathematics, as well as being able to identify what makes an exceptional math teacher who is able to address the needs of all students. 25 Level 1 Field Experience hours required. Offered during Spring term.

This course is designed to help students conceptualize issues and opportunities in teaching their disciplinary content to diverse students and in different classroom contexts. Up to ten hours of community-based service/observation required. In this course, students will analyze and reflect on how teaching in their disciplines is informed by diverse cultures of schooling and youth, including the influences of economic, social, cultural, political, gender, and religious factors on schooling, educational policy and opportunity. Students will use disciplinary content to critically and creatively reflect on the teaching of that content in secondary schools. Students will be introduced to issues and ways of presenting essential disciplinary content in ways that engage diverse learners, including learners who have not been served well by formal education. Students will also develop a theory of teaching that emphasizes the intersection of disciplinary content with multicultural perspectives. Offered during Spring term only.

(JYEL CREDIT) This course is an invitation to secondary education as a profession, an opportunity for students considering education as a career to explore the reality of teaching and learning a disciplinary content area in a variety of Chicago-area schools. Students will become familiar with different narratives of teaching through teacher and student biographies, testimonials, literature, film, and classroom observations. They will explore the interrelationships between, for example, popular cultural beliefs about schooling; teacher and student identities; and classroom interaction. The instructor will coordinate observations in several classrooms as the basis for intensive, guided reflective work, aimed at supporting students' initial and subsequent efforts of developing identities as disciplinary content educators (25 hours of high school classroom observation required). Course is also an introduction to the TEACH Program. Offered during Fall, Winter, and Spring terms.

The first quarter of a 3-quarter sequence. Topics in the sequence include the integers; abstract groups, rings, and fields; polynomial rings; isomorphism theorems; extension fields; and an introduction to Galois theory. MAT 303 is highly recommended.

A study of properties of integers: divisibility; Euclid's Algorithm; congruences and modular arithmetic; Euler's Theorem; Diophantine equations; distribution of primes; RSA cryptography.

A continuation of topics from MAT 310: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.

Incidence and separation properties of planes; congruences; the parallel postulate; area theory; ruler and compass construction.

Introduction to solid geometry and noneuclidean geometry (hyperbolic and spherical models); other special topics.

Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.

Probability spaces, combinatorial probability methods, discrete and continuous random variables and distributions, moment generating functions, development and applications of the classical discrete and continuous distributions.

History of mathematics with problem solving.

Introduction to statistical software (which will be used throughout the course). Descriptive statistics; elementary probability theory; discrete and continuous probability models; principles of statistical inference; Simple linear regression and correlation analysis.

Vectors, dot and cross products, lines and planes, cylinders and quadric surfaces, vector-valued functions, parametrization of plane curves and three dimensional curves, arc length, curvature and normal vector, functions of several independent variables, partial derivatives, the chain rule, directional derivatives, differentials, extreme values.

Lagrange multipliers, double and iterated integrals, area by double integrals, triple integrals, triple integrals in cylindrical and spherical coordinates, line integrals, vector fields, conservative vector fields and potential functions, Green?s Theorem, surface integrals, Stokes? Theorem, Gauss? Theorem.

Systems of linear equations and matrices; vectors in n-space; vector spaces: linear combinations, linear independence, basis; linear transformations, change of basis, eigenvalues and eigenvectors.

Intermediate programming in Java and problem solving. Writing Java programs with multiple classes: constructors, visibility modifiers, static members, accessor and mutator methods, and arrays of objects. Inheritance, polymorphism, and interfaces. Sorting arrays of primitive data and arrays of objects. Exception handling. (Not for CS majors) PREREQUISITE(S): CSC 211.

This is an intermediate programming course in C++, intended as a follow-up course to CSC 261. Topics include object-oriented programming, user-defined classes and objects, constructors, C++ memory management including pointers and dynamic allocation, copy constructors, destructors, and operator overloading. The course will also cover inheritance and polymorphism. Optional topics, as time allows, will include templates and the C++ Standard Template Library. PREREQUISITE(S): CSC 261

An introduction to basic concepts and techniques used in higher mathematics courses: set theory, equivalence relations, functions, cardinality, techniques of proof in mathematics. The emphasis is on problem solving and proof construction by students. The department recommends that students take this course no later than the spring quarter of the sophomore year.

Combinatorics, graph theory, propositional logic, singly-quantified statements, operational knowledge of set theory, functions, number systems, methods of direct and indirect proof.

Methods of direct and indirect proof, set theoretic proofs, sequences, mathematical induction, recursion, multiply-quantified statements, relations and functions, complexity.

Limits, continuity, the derivative, rules of differentiation, applications of the derivative, extrema, curve sketching, and optimization. This course meets for an additional 1.5-hour lab session each week for enrichment and problem solving.

Definite and indefinite integrals, the Fundamental Theorem of Calculus, applications of the integral, exponential and logarithmic functions, inverse trigonometric functions, techniques of integration. This course meets for an additional 1.5-hour lab session each week for enrichment and problem solving.

L'Hopital's rule, improper integrals, sequences and series, Taylor polynomials. This course meets for an additional 1.5-hour lab session each week for enrichment and problem solving.

Limits, continuity, the derivative, rules of differentiation, and applications, with precalculus review included for each topic. The full MAT 147-8-9 sequence covers all the material of MAT 150-1-2 plus additional precalculus material.

Extrema, curve sketching, related rates, definite and indefinite integrals, applications of the integral, exponential and logarithmic functions, with precalculus review included for each topic.

Techniques of integration, L'Hopital's rule, improper integrals, Taylor polynomials, series and sequences, first-order differential equations, with precalculus review included for each topic.

Limits, continuity, the derivative, rules of differentiation, applications of the derivative, extrema, curve sketching, and optimization. Course meets for an additional 1.5 hour lab session each week in order to cover the material in greater depth. Students considering a math major are advised to take the 160 or 170 sequence.

Definite and indefinite integrals, the Fundamental Theorem of Calculus, applications of the integral, exponential and logarithmic functions, inverse trigonometric functions, techniques of integration. Course meets for an additional 1.5 hour lab session each week in order to cover the material in greater depth.

L'Hopital's rule, improper integrals, sequences and series, Taylor polynomials. Course meets for an additional 1.5 hour lab session each week in order to cover the material in greater depth.

The course covers the following topics using examples from the sciences: Functions as models, logarithmic scale graphing, exponential growth and decay, difference equations and limits of sequences, geometric series, functions and limits, trigonometric functions and their limits, continuity, limits at infinity, the derivative, differentiation rules, derivatives of trigonometric and exponential functions, related rates, derivatives of inverse and logarithm functions. Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course. Students majoring in the sciences should consult with their major department to decide between the 160 and 170 sequences.

The course covers the following topics using examples from the sciences: Applications of the derivative including approximation and local linearity, differentials, extrema and the Mean Value Theorem, monotonicity and concavity, extrema, inflection points, graphing, L'Hospital's Rule, optimization, and the Newton-Raphson method, antiderivaties, the definite integral, Riemann sums, the Fundamental Theorem of Calculus, area, cumulative change, average value of a function, and techniques of integration: substitution rule and integration by parts. Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course. Course meets for an additional lab session each week during which time students will work on applied mathematics projects based on the topics covered in the course.