# Mathematics

## Mathematics Placement

For students to succeed in mathematics courses, it is important that they have the proper background. Students will be placed into their first math course at USD based on their SAT/ACT score. A student may take our mathematics placement exam in order to be placed into a higher level course than the SAT/ACT score will allow. Students can take the placement exam at most twice during any 12 month period.

An exception to the above is: students who have either 1) scored 3 or higher on an AP calculus exam; 2) transferred a course that satisfies USD’s core curriculum mathematical competency requirement; or 3) earned 4 or higher on the HL5 IB exam or 3 or higher on the SL5 IB exam will have fulfilled their core mathematics requirement, and will be placed into future mathematics courses at USD based on those scores.

## The Mathematics Major

The program in mathematics has a threefold objective: to provide courses giving technical mathematical preparation to students in any field of academic endeavor; to provide liberal arts courses which will demonstrate our mathematical heritage from past ages, and point out the impact of mathematical thought and philosophy on our culture in this technological civilization; and to provide courses of advanced mathematical knowledge which will prepare students for graduate work or professional employment in mathematics or related areas.

## The Mathematics Major

### Preparation for the Major

Code | Title | Units |
---|---|---|

COMP 150 | Computer Programming I | 3 |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 160 | Logic for Mathematics and Computer Science ^{1} | 3 |

MATH 250 | Calculus III | 4 |

PHYS 270 & 270L | Introduction to Mechanics and Mechanics Lab | 4 |

Select one of the following: | 3-4 | |

Computer Programming II | ||

Introduction to Electricity and Magnetism and Introduction to Electricity and Magnetism Lab | ||

Total Units | 25-26 |

### Major Requirements

In order to obtain a major in mathematics, the student must satisfy the core curriculum requirements as set forth in this course catalog and complete the following courses:

Code | Title | Units |
---|---|---|

MATH 320 | Linear Algebra | 3 |

MATH 360 | Real Analysis I | 3 |

Select one of the following: | 3 | |

Probability | ||

Real Analysis II | ||

Geometry | ||

Select one of the following: | 3 | |

Algebraic Systems | ||

Topology | ||

Select 12 units of upper-division mathematics electives chosen from courses numbered above 300, excluding 305 (Seminar in Teaching Mathematics), 405 (Advanced Perspectives) and 498 (Internship) | 12 | |

Total Units | 24 |

At least 15 of the upper-division units in the major must be completed at USD.

### Recommended Program of Study, Mathematics

Freshman Year | ||
---|---|---|

Semester I | Units | |

Preceptorial | 3-4 | |

COMP 150 | Computer Programming I | 3 |

MATH 150 | Calculus I | 4 |

MATH 118 | Essentials of Trigonometry (if needed) | 1 |

CC | 6 | |

Semester II | ||

MATH 151 | Calculus II | 4 |

MATH 160 | Logic for Mathematics and Computer Science | 3 |

PHYS 270 & 270L | Introduction to Mechanics | 4 |

CC | 3 or 6 | |

Sophomore Year | ||

Semester I | ||

MATH 250 | Calculus III | 4 |

COMP 151 or PHYS 271 PHYS 271Land | Computer Programming II Introduction to Electricity and Magnetism Introduction to Electricity and Magnetism Lab | 3-4 |

CC | 6-9 | |

Semester II | ||

MATH 320 | Linear Algebra | 3 |

CC | 12-15 | |

Junior Year | ||

Semester I | ||

Upper-Division MATH | 6 | |

CC, Minor, or electives | 9-12 | |

Semester II | ||

Upper-Division MATH | 6 | |

CC, Minor, or electives | 9-12 | |

Senior Year | ||

Semester I | ||

Upper-Division MATH | 6 | |

CC, Minor, or electives | 9-12 | |

Semester II | ||

Upper-Division MATH | 3 | |

CC, Minor, or electives | 12-15 |

## Secondary Education Emphasis

Students interested in obtaining the Single Subject Teaching Credential in mathematics are required to major in mathematics with a secondary education emphasis.

### Preparation for the Major

Code | Title | Units |
---|---|---|

COMP 150 | Computer Programming I | 3 |

MATH 115 | College Algebra (or pass the Level 2 placement exam) | 3 |

MATH 120 | Introduction to Statistics | 3 |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 160 | Logic for Mathematics and Computer Science ^{1} | 3 |

MATH 250 | Calculus III | 4 |

PHYS 270 & 270L | Introduction to Mechanics and Mechanics Lab | 4 |

Total Units | 28 |

### Major Requirements

For the mathematics major with secondary education emphasis, the student must satisfy the core curriculum requirements and complete the following courses:

Code | Title | Units |
---|---|---|

MATH 305 | Seminar in Teaching Mathematics | 2 |

MATH 320 | Linear Algebra | 3-4 |

MATH 325W | History of Mathematics | 3 |

MATH 350 | Probability | 3 |

MATH 360 | Real Analysis I | 3 |

MATH 375 | Algebraic Systems | 3 |

MATH 380 | Geometry | 3 |

MATH 405 | Advanced Perspective on High School Mathematics | 3 |

Select 6 units of Upper-Division Mathematics Electives (chosen from courses numbered above 300) | 6 | |

Total Units | 29-30 |

At least 15 of the Upper-Division units in the major must be completed at USD.

To obtain the professional preliminary teaching credential, consult the School of Leadership and Education Sciences for further requirements.

### Recommended Program of Study Mathematics, Secondary Education Emphasis

Freshman Year | ||
---|---|---|

Semester I | Units | |

Preceptorial | 3 | |

MATH 115 or 150 | College Algebra Calculus I | 4 |

MATH 118 | Essentials of Trigonometry (if needed) | 1 |

CC | 9 | |

Semester II | ||

MATH 120 | Introduction to Statistics | 3 |

MATH 150 or 151 | Calculus I Calculus II | 4 |

COMP 150 | Computer Programming I | 3 |

CC | 6 | |

Sophomore Year | ||

Semester I | ||

MATH 151 or 250 | Calculus II Calculus III | 4 |

MATH 160 | Logic for Mathematics and Computer Science | 3 |

MATH 305 | Seminar in Teaching Mathematics | 2 |

CC and electives | 6-9 | |

Semester II | ||

MATH 250 | Calculus III | 4 |

MATH 320 | Linear Algebra | 3 |

PHYS 270 | Introduction to Mechanics | 3 |

CC, SOLES, and electives | 6-9 | |

Junior Year | ||

Semester I | ||

Upper-Division MATH | 6 | |

CC, SOLES, and electives | 9-12 | |

Semester II | ||

Upper-Division MATH | 6 | |

CC, SOLES, and electives | 9-12 | |

Senior Year | ||

Semester I | ||

Upper-Division MATH | 6 | |

CC, SOLES, and electives | 9-12 | |

Semester II | ||

Upper-Division MATH | 6 | |

CC, SOLES, Minor, and electives | 9-12 |

## Applied Emphasis

The mathematics department also offers a major in mathematics with an applied emphasis.

### Preparation for the Major

Code | Title | Units |
---|---|---|

COMP 150 | Computer Programming I | 3 |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 160 | Logic for Mathematics and Computer Science | 3 |

MATH 250 | Calculus III | 4 |

PHYS 270 & 270L | Introduction to Mechanics and Mechanics Lab | 4 |

Total Units | 22 |

### Major Requirements

For the mathematics major with applied emphasis, the student must satisfy the core curriculum requirements and complete the following courses:

Code | Title | Units |
---|---|---|

MATH 320 | Linear Algebra | 3-4 |

MATH 330 | Ordinary Differential Equations | 3 |

MATH 340 | Numerical Analysis I | 3 |

MATH 350 | Probability | 3 |

MATH 445 | Mathematical Modeling | 3 |

MATH 495W | Senior Project A | 1 |

MATH 496W | Senior Project B | 2 |

Select two of the following: ^{2} | 6 | |

Partial Differential Equations | ||

Numerical Analysis II | ||

Mathematical Statistics | ||

Real Analysis I | ||

Complex Function Theory | ||

One additional upper-division elective (chosen from courses numbered above 300 except for MATH 305, MATH 405, and MATH 498) | 3 | |

Total Units | 27-28 |

At least 15 of the upper-division units in the major must be completed at USD.

Substitutions in this list may be granted with the approval of the department chair.

For the applied emphasis, a minor in a natural science, engineering, or economics is also required. Other minors can be substituted but require a proposal from the student explaining the connection between that discipline and mathematics that must be approved in advance by the department chair.

^{1} | Students are encouraged to complete MATH 160 before taking MATH 320. In addition, students are strongly advised to complete both MATH 160 and MATH 320 before taking upper division courses numbered above 331. MATH 160 satisfies the core curriculum logic competency requirement. Students majoring in mathematics should take this course instead of PHIL 101 or PHIL 102. |

^{2} | Students planning to go to graduate school are advised to take MATH 360. |

### Recommended Program of Study Mathematics, Applied Emphasis

Freshman Year | ||
---|---|---|

Semester I | Units | |

Preceptorial | 3 | |

MATH 150 | Calculus I | 4 |

MATH 118 | Essentials of Trigonometry (if needed) | 1 |

CC | 9 | |

Semester II | ||

MATH 151 | Calculus II | 4 |

PHYS 270 | Introduction to Mechanics | 3 |

MATH 160 | Logic for Mathematics and Computer Science | 3 |

CC | 3-6 | |

Sophomore Year | ||

Semester I | ||

MATH 250 | Calculus III | 4 |

COMP 150 | Computer Programming I | 3 |

CC and electives | 9 | |

Semester II | ||

MATH 320 | Linear Algebra | 3 |

CC and electives | 9-12 | |

Junior Year | ||

Semester I | ||

MATH 330 | Ordinary Differential Equations | 3 |

MATH 350 | Probability | 3 |

CC, Minor, and electives | 9-12 | |

Semester II | ||

Upper-Division MATH | 6 | |

CC, Minor, and electives | 9-12 | |

Senior Year | ||

Semester I | ||

MATH 445 | Mathematical Modeling | 3 |

MATH 495W | Senior Project A | 1 |

Upper-Division MATH | 3 | |

CC, Minor, and electives | 9 | |

Semester II | ||

MATH 496W | Senior Project B | 2 |

Upper-Division MATH | 3 | |

CC, Minor, and electives | 9-12 |

### Recommended Program of Study: Integrated Teacher Preparation Program (ITPP) Pathway

The Integrated Teacher Preparation Program (ITPP) provides paths to 4-year science and math degrees that include a teaching credential and preparation for the California Subject Examination for Teachers (CSET). Students who are interested in middle or secondary education (grades 6-12) in California may earn a degree in mathematics while simultaneously completing requirements for a teaching credential. The degree integrates content knowledge and laboratory practices in the discipline, evidence-based teaching/learning theories, teaching performance expectations, and pre-student teaching clinical practice while satisfying baccalaureate degree requirements and CTC single subject credential program standards. There is some flexibility to meet individual needs. Students are encouraged to consult the ITPP website (http://www.sandiego.edu/itpp) and advisors (itpp@sandiego.edu) to ensure that their needs and interests will be met.

In addition to all courses for the mathematics major, students completing the ITPP pathway must also take the following:

Code | Title | Units |
---|---|---|

EDUC 332P | Curriculum and Methods of Teaching in Today's Global Secondary Classrooms | 3 |

EDUC 334P | Methods of Teaching Literacy in Secondary Schools in a Global Society | 3 |

EDUC 337P | Foundations in Curriculum and Instruction Theory: Secondary Praxis in Historical Context | 3 |

EDUC 381C | Multicultural and Philosophical Foundations in a Global Society | 3 |

EDUC 382 | Psychological Foundations of Education in a Diverse Society | 3 |

EDUC 384C | Methods of Teaching English Language and Academic Development in Crosscultural Contexts | 3 |

EDUC 491P | Student Teaching for the Single Subject Credential | 9 |

EDUC 491S | Student Teaching Seminar for the Single Subject Credential | 3 |

EDSP 389P | Healthy Environments and Inclusive Education in a Global Society | 3 |

The following paradigm is included as a guide only, and should not be interpreted in a rigid sense. UD elective courses may be taken at any time as long as the course prerequisites have been satisfied.

## The Mathematics Minor

Students may obtain a minor in mathematics by completing 18 units of mathematics course work. These units must include:

Code | Title | Units |
---|---|---|

6 units of upper division work | 6 | |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 160 | Logic for Mathematics and Computer Science | 3-4 |

or MATH 250 | Calculus III | |

Total Units | 18 |

MATH 090 | INTERMEDIATE ALGEBRA

Units: 3

A survey of basic algebraic skills for students with insufficient mathematics preparation. This remedial course counts for “work-load credit” only. That is, its three units are counted as part of the student’s load during the semester in which it is taken, and the grade earned in the course is included in the computation of the student’s grade point average, but it does not satisfy any core curriculum requirement, or for the major or minor in mathematics, and it does not count toward the 124 units required for graduation.

MATH 112 | INVESTIGATIONS IN MODERN MATHEMATICS

Units: 3 Repeatability: No

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 090

This core curriculum mathematics course provides a less algebraic alternative to MATH 115 for those students who need to fulfill the mathematical competency requirement, but who are not planning to go on in math. Topics may include: voting theory, graph theory, sequences, population growth, fractals, topology, geometry, and recursion. Note 1: This course does not serve as a prerequisite to MATH 120, MATH 130, MATH 150, or MATH 200.

MATH 115 | COLLEGE ALGEBRA

Units: 3 Repeatability: No

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 090

Review of exponents, equations, and inequalities; function notation, composition, and inverses; linear, quadratic, polynomial, exponential, and logarithmic functions and their graphs.

MATH 118 | ESSENTIALS OF TRIGONOMETRY

Units: 1

Definitions, solutions of right triangles, graphs, identities, and inverse trigonometric functions.

MATH 120 | INTRODUCTION TO STATISTICS

Units: 3 Repeatability: No

Core Attributes: Quantitative reasoning comp

Prerequisites: MATH 115 or MATH 130 or MATH 150

Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference.

MATH 130 | SURVEY OF CALCULUS

Units: 3 Repeatability: No

Core Attributes: First year Integration, Math reasng and prob solving

Prerequisites: Passing the appropriate departmental placement test within the previous year or Passing the appropriate departmental placement test within the previous year or MATH 115

A terminal mathematics course giving an introduction to the concepts and techniques of elementary differential and integral calculus. Note 1: This course is not equivalent to MATH 150, and does not serve as a prerequisite to MATH 151. Prereq: MATH 115 with a grade of C- or better, or pass Level 2 mathematics placement exam (2MTH or 3MTH).

MATH 150 | CALCULUS I

Units: 4 Repeatability: No

Core Attributes: First year Integration, Math reasng and prob solving

Prerequisites: MATH 115 or Passing the appropriate departmental placement test within the previous year

Fundamental notions of analytic geometry, differential and integral calculus with elementary applications; historical references.

MATH 151 | CALCULUS II

Units: 4 Repeatability: No

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 150

Continuation of Calculus I including integration, infinite series, differential equations, applications, and historical references.

MATH 160 | LOGIC FOR MATHEMATICS AND COMPUTER SCIENCE

Units: 3 Repeatability: No

Core Attributes: Math reasng and prob solving

Prerequisites: Passing the appropriate departmental placement test within the previous year or MATH 115 or MATH 130 or MATH 150 or MATH 151 or MATH 250

Propositional calculus; first-order predicate calculus, mathematical proof, mathematical induction, fundamental set theory, relations and functions, and applications to problems in mathematics and computer science.

MATH 200 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS I

Units: 3 Repeatability: No

Prerequisites: MATH 115 or MATH 130 or MATH 150

Problem solving, sets, numeration systems, a development of the whole number system, geometric figures, and computers. Note: This course does not count toward either the major or minor in mathematics.

MATH 222 | DISCRETE MATHEMATICS

Units: 3 Repeatability: No

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 151 or (MATH 150 and ENGR 121 or COMP 150)

Our world is inundated with discrete packets of data, from satellite imaging, to cyber security, to biotechnology. A language and framework is needed to understand, quantify, and manipulate this information. This course provides the tools (mathematical proof techniques) and case studies (sets and infinity, numbers and encryption, graphs and structure) to equip us for our data driven world.

MATH 250 | CALCULUS III

Units: 4

Prerequisites: MATH 151

Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references. Prereq: MATH 151 with a grade of C– or better.

MATH 294 | SPECIAL TOPICS

Units: 3 Repeatability: No

Prerequisites: MATH 151

Topics of special interest chosen by the instructor.

MATH 300 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS II

Units: 3

Prerequisites: MATH 200

Measurement concepts, development of the real number system, algebra, geometric mappings, probability, and statistics. Note: This course does not count toward either the major or minor in Mathematics. Prereq: MATH 200 with a grade of C– or better.

MATH 305 | SEMINAR IN TEACHING MATHEMATICS

Units: 2

Senior seminar for single subject credential students in mathematics. Issues in mathematics education including: Contribution to mathematics by men and women of various ethnic, racial, and cultural groups; equity considerations in mathematics education; variations in how students learn mathematics; diverse methods of communication and assessment in mathematics; and practical aspects of teaching diverse students. Students will be required to do some tutoring in mathematics. This course does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).

MATH 310 | APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING I

Units: 3 Repeatability: No

Prerequisites: MATH 151

Matrix algebra, ordinary differential equations, and operational techniques. Students may not receive credit for both MATH 310 and MATH 330 (mutually exclusive).

MATH 311 | APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING II

Units: 3-4

Prerequisites: MATH 250 and MATH 310

Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prereq: MATH 250 and 310. Students may not take MATH 311 concurrently with MATH 331 or after having taken MATH 331.

MATH 315 | APPLIED PROBABILITY AND STATISTICS

Units: 3

Prerequisites: MATH 250

Introduction to probability; discrete and continuous random variables; conditional and joint distributions and densities; functions of random variables; expectation and estimation; central limit theorem; introduction to statistics; introduction to random sequences and random processes.

MATH 320 | LINEAR ALGEBRA

Units: 3-4

Prerequisites: MATH 151

Systems of linear equations, matrix algebra and operations, vector spaces of three or more dimensions, linear independence, inner product spaces, linear transformations and their matrices, determinants, eigenvalues and eigenvectors, and brief introduction to canonical forms. Prereq: MATH 151 with a grade of C- or better. It is recommended that students take MATH 160 before taking MATH 320.

MATH 325W | HISTORY OF MATHEMATICS

Units: 3

Core Attributes: Writing-Pre F17 CORE

Prerequisites: MATH 250

Selected topics from the history of mathematics. The course includes a variety of writing assignments. Emphasis is on the history of mathematical ideas, rather than on personalities or social background. Prereq: MATH 250 with a grade of C- or better.

MATH 330 | ORDINARY DIFFERENTIAL EQUATIONS

Units: 3

Prerequisites: MATH 250

Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications. Prereq: MATH 250 with a grade of C- or better.

MATH 331 | PARTIAL DIFFERENTIAL EQUATIONS

Units: 3

Prerequisites: MATH 330

Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prereq: MATH 330 with a grade of C- or better.

MATH 340 | NUMERICAL ANALYSIS I

Units: 3

Prerequisites: MATH 151 and COMP 150

Approximate computations and round-off errors, Taylor expansions, numerical solution of equations and systems of equations, numerical integration, numerical solution of differential equations, interpolation, and problem solving on the computer. Prereq: MATH 151 with a grade of C- or better and COMP 150 with a grade of C- or better. Cross-listed as COMP 340.

MATH 341 | NUMERICAL ANALYSIS II

Units: 3

Prerequisites: MATH 250 and MATH 320 and MATH 330 (Can be taken Concurrently) and MATH 340

Estimation of eigenvalues and eigenvectors of matrices; numerical solutions of differential equations, existence, and stability theory; and computer lab assignments. Prereq: MATH 250, 320, 330 (may be taken concurrently), and 340, all with a grade of C- or better. Cross-listed as COMP 341.

MATH 350 | PROBABILITY

Units: 3

Prerequisites: MATH 250

Probability axioms, conditional probability, discrete and continuous sample spaces, random variables and common distributions, jointly distributed random variables, and central limit theorem.

MATH 351 | MATHEMATICAL STATISTICS

Units: 3

Prerequisites: MATH 350

Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prereq: MATH 350 with a grade of C- or better.

MATH 355 | COMBINATORICS

Units: 3

Prerequisites: MATH 151 and MATH 160

Principles of enumeration, finite difference calculus, generating functions, finite difference equations, principle of Inclusion and Exclusion, introduction to the theory of combinatorial graphs, and applications to computer science. Prereq: MATH 151 with a grade of C- or better and MATH 160 with a grade of C- or better.

MATH 360 | REAL ANALYSIS I

Units: 3

Prerequisites: MATH 160 and MATH 250

A study of the foundations of real analysis, including the calculus of functions of one and several variables, infinite processes, convergence theory, and selected topics of advanced undergraduate analysis. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

MATH 361 | REAL ANALYSIS II

Units: 3

Prerequisites: MATH 360

A study of the foundations of real analysis, including the calculus of functions of one and several variables, infinite processes, convergence theory, and selected topics of advanced undergraduate analysis. Prereq: MATH 360 with a grade of C- or better.

MATH 365 | COMPLEX FUNCTION THEORY

Units: 3

Prerequisites: MATH 160 and MATH 250

Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

MATH 370 | THEORY OF NUMBERS

Units: 3

Prerequisites: MATH 151 and MATH 160

Divisibility, Euclidean algorithm, fundamental theorem of arithmetic, congruences, Fermat’s theorem, Euler’s function, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic residues, reciprocity law, and continued fractions. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

MATH 375 | ALGEBRAIC SYSTEMS

Units: 3

Prerequisites: MATH 151 and MATH 160

An introduction to groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and applications of these systems to other branches of mathematics. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

MATH 380 | GEOMETRY

Units: 3

Prerequisites: MATH 160 and MATH 250

An introduction to an area of modern geometry. The specific topic will be chosen from the following: non-Euclidean geometry, differential geometry, projective geometry, or metric geometry, and historical references. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

MATH 385 | TOPOLOGY

Units: 3

Prerequisites: MATH 160 and MATH 250

Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

MATH 388 | MATHEMATICAL LOGIC

Units: 3

Prerequisites: MATH 160 and MATH 151

Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

MATH 395 | MATHEMATICAL PROBLEM SOLVING SEMINAR

Units: 1 Repeatability: Yes (Can be repeated for Credit)

Prerequisites: MATH 151

This course is intended for students who enjoy the challenge of mathematical problems. This course differs from other mathematics courses which are focused on the theory and applications of a single branch of mathematics. It emphasizes problem-solving techniques, creative thinking, and exposition of skills in different areas of mathematics such as algebra, calculus, geometry, and number theory. (May be taken twice for credit.).

MATH 405 | ADVANCED PERSPECTIVE ON HIGH SCHOOL MATHEMATICS

Units: 3

This course is a required course in the Mathematics Single Subject credential program. It provides a capstone experience for future mathematics high school teachers, in which they look at topics in high school mathematics from an advanced viewpoint. Connections between mathematics topics and between basic and more advanced mathematics will be emphasized. This course does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).

MATH 444 | FORUM

Units: 3 Repeatability: No

Core Attributes: Advanced writing competency, Oral communication competency

Prerequisites: MATH 355 (Can be taken Concurrently) or MATH 360 (Can be taken Concurrently) or MATH 365 (Can be taken Concurrently) or MATH 370 (Can be taken Concurrently) or MATH 375 (Can be taken Concurrently) or MATH 380 (Can be taken Concurrently) or MATH 385 (Can be taken Concurrently)

The goal of this capstone mathematics course is to improve the ability to communicate mathematics, both written and oral, to a general and technical audience. In the process, students are exposed to a broad range of topics from modern and classical mathematics, and increase their familiarity with the culture of mathematics. This course fulfills the upper division writing and oral communication requirements.

MATH 445 | MATHEMATICAL MODELING

Units: 3

Prerequisites: MATH 250 and MATH 320 and MATH 330

The construction and analysis of mathematical models, simplifying assumptions and testing strategies; topics chosen by the instructor in dimensional analysis, discrete and continuous dynamical systems, stochastic models, linear systems, optimization models, statistical methods, and graph theory. Prereq: MATH 250 with a grade of C- or better, MATH 320 with a grade of C- or better and MATH 330 with a grade of C- or better.

MATH 494 | SPECIAL TOPICS

Units: 1-4 Repeatability: Yes (Can be repeated for Credit)

Prerequisites: MATH 250

Topics of special interest chosen by the instructor. May be repeated for credit with the consent of the instructor.

MATH 495W | SENIOR PROJECT A

Units: 1 Repeatability: No

Core Attributes: Writing-Pre F17 CORE

Prerequisites: MATH 250 and MATH 320

Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets once per week: prepare a written research proposal for work to be carried out in MATH 496W; ongoing written and oral progress reports and regular consultation with the faculty supervisor.

MATH 496W | SENIOR PROJECT B

Units: 2

Core Attributes: Writing-Pre F17 CORE

Prerequisites: MATH 495W

Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets twice per week: carry out the project defined in MATH 495W; ongoing written and oral progress reports and regular consultation with the faculty supervisor; final written and oral presentation in the presence of other students and faculty. Prereq: MATH 495W with a grade of C– or better.

MATH 498 | INTERNSHIP

Units: 1-3 Repeatability: Yes (Can be repeated for Credit)

Core Attributes: Law - Experiential

Practical experience in the application of mathematics. Students will be involved in projects conducted by businesses, agencies, and institutions. Enrollment is arranged on an individual basis according to the student’s interest and background, and the availability of positions. A written report is required. Units may not normally be applied toward the major or minor in mathematics. MATH 498 may be repeated for a total of three units.

MATH 499 | INDEPENDENT STUDY

Units: 1-3 Repeatability: Yes (Can be repeated for Credit)

Core Attributes: Law - Experiential

Student reading and research in selected special topics; student presentations. May be repeated for credit once with a different topic.

## CHAIR

Lynn McGrath, PhD

## Faculty

Dwight R. Bean, PhD

Adam Boocher, PhD

Amy Buchmann, PhD

Satyan L. Devadoss, PhD

Jane E. Friedman, PhD

Jennifer Gorsky, PhD

Diane Hoffoss, PhD

Stacy Langton, PhD

Luby Liao, PhD

Perla Myers, PhD

Cameron Parker, PhD

Jack W. Pope, PhD

Candice Price, PhD

Lukasz Pruski, PhD

Amanda Ruiz, PhD

Michael Shulman, PhD

Ani Velo, PhD