Students entering the University of San Diego and/or declaring a major during 2020-2021, should follow information contained in the printed course catalog (also known as the "catalog of record") published on April 1, 2020. Access the catalog of record at https://catalogs.sandiego.edu.

## The Mathematics Major

### Preparation for the Major

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

MATH 110 | Investigations in Mathematics | 3-3.5 |

or MATH 112 | ||

or MATH 120 | Introduction to Statistics | |

or COMP 110 | Computational Problem Solving | |

or COMP 150 | Computer Programming I | |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 250 | Calculus III | 4 |

MATH 260 | Foundations of Higher Mathematics | 3 |

or MATH 262 | Discrete Mathematics | |

or MATH 222 | ||

or MATH 160 | ||

Total Units | 18-18.5 |

### 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 | 3 |

MATH 375 | Abstract Algebra | 3 |

Select 15 units of upper-division electives except for Math 300, 305, 405, and 498. | 15 | |

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 | |

LLC Class | 3-4 | |

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

MATH 110, MATH 112, MATH 120, or COMP 110 | Investigations in Mathematics Introduction to Statistics Computational Problem Solving | 3-3.5 |

MATH 150 | Calculus I | 4 |

CC | 3 | |

Semester II | Hours | |

MATH 151 | Calculus II | 4 |

MATH 260, 262, MATH 222, or MATH 160 | Foundations of Higher Mathematics Discrete Mathematics | 3 |

CC | 6-9 | |

Sophomore Year | ||

Semester I | Hours | |

MATH 250 | Calculus III | 4 |

MATH 320 | Linear Algebra | 3 |

CC | 6-9 | |

Semester II | Hours | |

MATH 360 | Real Analysis | 3 |

CC, Minor, Electives | 12-15 | |

Junior Year | ||

Semester I | Hours | |

MATH 375 | Abstract Algebra | 3 |

Upper-Division MATH | 3 | |

CC, Minor, Electives | 9-12 | |

Semester II | Hours | |

Upper-Division MATH | 3 | |

CC, Minor, Electives | 9-12 | |

Senior Year | ||

Semester I | Hours | |

Upper-Division MATH | 6 | |

CC, Minor, Electives | 9-12 | |

Semester II | Hours | |

Upper-Division MATH | 3 | |

CC, Minor, 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 |
---|---|---|

MATH 120 | Introduction to Statistics | 3-3.5 |

or COMP 110 | Computational Problem Solving | |

MATH 150 | Calculus I | 4 |

MATH 151 | Calculus II | 4 |

MATH 250 | Calculus III | 4 |

MATH 260 | Foundations of Higher Mathematics | 3 |

or MATH 262 | Discrete Mathematics | |

or MATH 222 | ||

or MATH 160 | ||

Total Units | 18-18.5 |

### 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 |

MATH 330 | Ordinary Differential Equations | 3 |

MATH 360 | Real Analysis | 3 |

MATH 375 | Abstract Algebra | 3 |

MATH 444 | Forum | 3 |

MATH 445 | Mathematical Modeling | 3 |

Select 6 units of upper-division electives except for Math 300, 305, 405, and 498. | 6 | |

Total Units | 24 |

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

^{1} | Students are strongly advised to complete MATH 320 before taking upper-division courses numbered above 330. |

### Recommended Program of Study: Applied Emphasis

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

Semester I | Units | |

LLC Class | 3-4 | |

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

MATH 120 or COMP 110 | Introduction to Statistics Computational Problem Solving | 3-3.5 |

MATH 150 | Calculus I | 4 |

CC | 3 | |

Semester II | Hours | |

MATH 151 | Calculus II | 4 |

MATH 260, 262, MATH 222, or MATH 160 | Foundations of Higher Mathematics Discrete Mathematics | 3 |

CC | 6-9 | |

Sophomore Year | ||

Semester I | Hours | |

MATH 250 | Calculus III | 4 |

MATH 320 | Linear Algebra | 3 |

CC | 6-9 | |

Semester II | Hours | |

MATH 330 | Ordinary Differential Equations | 3 |

MATH 360 | Real Analysis | 3 |

CC , Minor, Electives | 9-12 | |

Junior Year | ||

Semester I | Hours | |

MATH 375 | Abstract Algebra | 3 |

MATH 444 | Forum | 3 |

CC, Minor, Electives | 9-12 | |

Semester II | Hours | |

MATH 445 | Mathematical Modeling | 3 |

CC, Minor, Electives | 9-12 | |

Senior Year | ||

Semester I | Hours | |

Upper-Division MATH | 6 | |

CC, Minor, Electives | 9-12 | |

Semester II | Hours | |

Upper-Division MATH | 3 | |

CC, Minor, Electives | 9-12 |

## 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 | ^{1} | 0-3 |

or MATH 260 | Foundations of Higher Mathematics | |

MATH 250 | Calculus III | 4 |

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

Total Units | 25-28 |

### 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 |

MATH 325 | History of Mathematics | 3 |

or MATH 325W | ||

MATH 350 | Probability | 3 |

MATH 360 | Real Analysis | 3 |

MATH 375 | Abstract Algebra | 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 |

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: Secondary Education Emphasis

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

Semester I | Units | |

LLC Class | 3 | |

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

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

CC | 9 | |

Semester II | Hours | |

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 | Hours | |

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

MATH 160 or MATH 260 | 3 | |

MATH 305 | Seminar in Teaching Mathematics | 2 |

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

Semester II | Hours | |

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 | Hours | |

Upper-Division MATH | 6 | |

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

Semester II | Hours | |

Upper-Division MATH | 6 | |

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

Senior Year | ||

Semester I | Hours | |

Upper-Division MATH | 6 | |

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

Semester II | Hours | |

Upper-Division MATH | 6 | |

CC, SOLES, 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 with a secondary education emphasis, students completing the ITPP pathway must also take the following teaching credential courses, following the Recommended Program of Study: Secondary Education Emphasis above.

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

EDTE 300P | Diversity, Inclusion & Schooling | 3 |

EDTE 301P | Methods for Language & Literacy | 3 |

EDTE 304P | Secondary Methods I | 3 |

EDTE 307P | Secondary Methods II: Mathematics | 3 |

EDTE 310P | Educational Psychology | 3 |

EDTE 311P | Equity & Advocacy in Educational Systems | 3 |

EDTE 312P | Methods for English Learners | 3 |

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

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

Students entering the University of San Diego and/or declaring a major during 2020-2021, should follow information contained in the printed course catalog (also known as the "catalog of record") published on April 1, 2020. Access the catalog of record at https://catalogs.sandiego.edu.

## The Mathematics Minor

Students may obtain a minor in mathematics by completing 21 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 250 | Calculus III | 4 |

MATH 260 | Foundations of Higher Mathematics | 3 |

or MATH 262 | Discrete Mathematics | |

Total Units | 21 |

Students entering the University of San Diego and/or declaring a major during 2020-2021, should follow information contained in the printed course catalog (also known as the "catalog of record") published on April 1, 2020. Access the catalog of record at https://catalogs.sandiego.edu.

MATH 090, MATH 110, MATH 115, MATH 118, MATH 120, MATH 130, MATH 150, MATH 151, MATH 200, MATH 250, MATH 260, MATH 262, MATH 294, MATH 300, MATH 305, MATH 310, MATH 311, MATH 315, MATH 320, MATH 325, MATH 330, MATH 331, MATH 340, MATH 341, MATH 350, MATH 351, MATH 355, MATH 360, MATH 361, MATH 365, MATH 370, MATH 375, MATH 380, MATH 385, MATH 388, MATH 395, MATH 405, MATH 440, MATH 444, MATH 445, MATH 494, MATH 496, MATH 498, MATH 499,

### 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.

Core Attributes: First Yr Integration (LC Only), Math reasng and prob solving

Prerequisites: MATH 090 or Passing the appropriate departmental placement test within the previous year or Passing the appropriate departmental placement test within the previous year or Passing the appropriate departmental placement test within the previous year

Mathematics is much more than calculation; it is an imaginative and creative endeavor that studies all sorts of patterns and structures, many of which are beautiful, intriguing, and applicable to the real world. This course will explore some surprising and rewarding mathematical ideas in areas that could include games, fractals, ciphers, elections, finance, risk measurement, the nature of infinity, or others. Along the way, students may confront issues that challenge their intuition, gain sharper analytical reasoning skills, and experience mathematical questions that have remained unsolved for hundreds of years. This course does not serve as a prerequisite to MATH 120, MATH 130, MATH 150, or MATH 200.

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 090 with a minimum grade of C- or Passing the appropriate departmental placement test within the previous year or Passing the appropriate departmental placement test within the previous year or Passing the appropriate departmental placement test within the previous year

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.

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.

Core Attributes: First Yr Integration (LC Only), 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 with a minimum grade of C-

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).

Core Attributes: First Yr Integration (LC Only), Math reasng and prob solving

Prerequisites: MATH 115 with a minimum grade of C- 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.

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 150 with a minimum grade of C-

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

### MATH 200 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS I

Units: 3 Repeatability: No

Prerequisites: MATH 115 with a minimum grade of C- or MATH 130 with a minimum grade of C- or MATH 150 with a minimum grade of C-

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 250 | CALCULUS III

Units: 4

Prerequisites: MATH 151 with a minimum grade of C-

Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references.

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 150

Mathematics is a creative endeavor based on reasoning, discovery and justification. In higher mathematics we explore, conjecture, and formally prove theorems about the behavior of abstract objects that model different aspects of reality. This course is an introduction and transition to the goals, tools, and subject matter of higher mathematics, including logic, the methods and structure of mathematical proof, mathematical induction, basic set theory, creative problem solving, and mathematical writing and communication. Students may not receive credit for taking both MATH 260 and MATH 262.

Core Attributes: Math reasng and prob solving

Prerequisites: MATH 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. Students may not receive credit for taking both MATH 260 and MATH 262.

### MATH 294 | SPECIAL TOPICS IN MATHEMATICS

Units: 0.5-4 Repeatability: Yes (Repeatable if topic differs)

Prerequisites: MATH 151 with a minimum grade of C-

Topics of special interest chosen by the instructor.

### MATH 300 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS II

Units: 3 Repeatability: No

Prerequisites: MATH 200 with a minimum grade of C

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.

### 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 with a minimum grade of C-

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 Repeatability: No

Prerequisites: MATH 250 with a minimum grade of C- and MATH 310 with a minimum grade of C-

Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis.

### 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 Repeatability: No

Prerequisites: MATH 260 with a minimum grade of C- or MATH 262 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C-

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.

### MATH 325 | HISTORY OF MATHEMATICS

Units: 3 Repeatability: No

Prerequisites: MATH 250 and (MATH 260 or MATH 160 or MATH 222 or MATH 262)

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.

### MATH 330 | ORDINARY DIFFERENTIAL EQUATIONS

Units: 3 Repeatability: No

Prerequisites: MATH 250 with a minimum grade of C- and (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-)

Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications.

### MATH 331 | PARTIAL DIFFERENTIAL EQUATIONS

Units: 3

Prerequisites: MATH 330 with a minimum grade of C-

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 Repeatability: No

Prerequisites: MATH 151 with a minimum grade of C- and (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and COMP 110 with a minimum grade of C-

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.

### MATH 341 | NUMERICAL ANALYSIS II

Units: 3

Prerequisites: MATH 250 with a minimum grade of C- and MATH 320 with a minimum grade of C- and MATH 330 with a minimum grade of C- (Can be taken Concurrently) and MATH 340 with a minimum grade of C-

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 Repeatability: No

Prerequisites: MATH 250 with a minimum grade of C- and (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-)

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 with a minimum grade of C-

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 Repeatability: No

Prerequisites: MATH 260 with a minimum grade of C- or MATH 262 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C-

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.

Core Attributes: Advanced writing competency

Prerequisites: MATH 260 with a minimum grade of C- or MATH 262 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C-

Analysis is the study of the foundations of calculus, including formal definitions of limits and convergence, and careful proofs of basic facts about numbers and functions. This course is an introduction to analysis of functions of one real variable.

### MATH 361 | TOPICS IN ANALYSIS

Units: 3 Repeatability: No

Prerequisites: MATH 360 with a minimum grade of C-

Analysis is the study of the foundations of calculus, including formal definitions of limits and convergence, and careful proofs of basic facts about numbers and functions. This course is a continuation of MATH 360.

### MATH 365 | COMPLEX FUNCTION THEORY

Units: 3 Repeatability: No

Prerequisites: (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and MATH 250 with a minimum grade of C-

Analytic function theory; power series, analytic continuation, conformal mapping, and applications.

### MATH 370 | THEORY OF NUMBERS

Units: 3 Repeatability: No

Prerequisites: (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and MATH 151 with a minimum grade of C-

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.

### MATH 375 | ABSTRACT ALGEBRA

Units: 3 Repeatability: No

Prerequisites: MATH 320 with a minimum grade of C-

Abstract algebra is the study of operations like addition and multiplication that act on objects other than numbers, such as vectors, matrices, polynomials, functions, transformations, and symmetries. This course is an introduction to the basic structures of abstract algebra: groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and their applications to other branches of mathematics.

### MATH 380 | GEOMETRY

Units: 3 Repeatability: No

Prerequisites: (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and MATH 250 with a minimum grade of C-

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.

### MATH 385 | TOPOLOGY

Units: 3 Repeatability: No

Prerequisites: (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and MATH 250 with a minimum grade of C-

Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness.

### MATH 388 | MATHEMATICAL LOGIC

Units: 3 Repeatability: No

Prerequisites: (MATH 260 with a minimum grade of C- or MATH 160 with a minimum grade of C- or MATH 222 with a minimum grade of C- or MATH 262 with a minimum grade of C-) and MATH 151 with a minimum grade of C-

Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic.

### MATH 395 | MATHEMATICAL PROBLEM SOLVING SEMINAR

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

Prerequisites: MATH 151 with a minimum grade of C-

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).

Core Attributes: Advanced Integration

Prerequisites: (MATH 160 or MATH 222) and (MATH 310 or MATH 330)

An introduction to mathematical applications to ecology. In this integrative course, students will learn to describe ecological processes in mathematical terms and formulate different types of mathematical models relevant to ecology. In a weekly lab, students from MATH 440 and EOSC 440 will work together on integrative projects and computer programming applications to mathematical ecology. Students may not receive credit for taking both MATH 440 and EOSC 440. Students may not receive credit for taking both MATH 440 and MATH 445.

Core Attributes: Advanced writing competency, Oral communication competency

Prerequisites: MATH 320 and (MATH 325 or MATH 330 or MATH 331 or MATH 340 or MATH 341 or MATH 350 or MATH 351 or MATH 355 or MATH 360 or MATH 361 or MATH 365 or MATH 370 or MATH 375 or MATH 380 or MATH 385 or MATH 388 or MATH 445)

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 with a minimum grade of C- and MATH 320 with a minimum grade of C- and MATH 330 with a minimum grade of C-

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 IN MATHEMATICS

Units: 0.5-4 Repeatability: Yes (Repeatable if topic differs)

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

Non-Core Attributes: Undergraduate Research

Independent research directed by a faculty member.

Non-Core Attributes: 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.

Non-Core Attributes: Experiential

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

Department of Mathematics

College of Arts and Sciences

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