# Mathematics

## Programs Offered

- Bachelor of Science in Mathematics
- Minor in Foundational Mathematics
- Minor in Mathematics
- Master of Science in Mathematics
- Approved CCTC Mathematics Subject Matter Waiver Program

Mathematics can be pursued as a scholarly discipline of an especially elegant and creative art form or it can be treated as a valuable tool in an applied discipline. Our program addresses both needs. Students will be given a strong background in mathematics and statistics as well as a substantial amount of interdisciplinary applications in Physics, Biostatistics, Business, Computer and Information Sciences, Computer Imagining or Artificial Intelligence.

## Careers

The mathematics major will prepare students for teaching careers, studies in graduate programs (in pure mathematics, applied mathematics, mathematics education, or the mathematical sciences) or for employment in high-tech and bio-tech industries, where mathematics-trained professionals with interdisciplinary expertise (sciences and business) are increasingly sought after.

## Program Learning Outcomes

Students graduating from the Mathematics program will be able to:

- Demonstrate critical thinking, problem solving skills and ability to use advanced mathematical methods by identifying,evaluating, classifying, analyzing, and synthesizing data and abstract ideas in various contexts and situations;
- Demonstrate the knowledge of current mathematical applications, computing practices and use of broad technology in industry, science and education;
- Demonstrate ability to use modern software, abstract thinking, and mathematical practices connected to scientific and industrial problems, and demonstrate these skills that are currently used by technologies in society and education;
- Perform skills that enable them to evaluate, propose and convey novel solutions to scientific and business problems, etc.;
- Demonstrate cooperation skills by working effectively with others in interdisciplinary group-settings - both inside and outside the classroom; and
- Demonstrate a sense of exploration that enables students to pursue lifelong learning and currency in their careers in mathematics, statistics, education, high-tech and bio-tech industries.

## Faculty

Ivona Grzegorczyk, Ph.D.

Professor of Mathematics

Chair, Mathematics Program

Academic Advisor for Mathematics and Single Subject Credential in Mathematics

Bell Tower West, Room 2275

(805) 437-8868

ivona.grze@csuci.edu

Geoffrey Buhl , Ph.D.

Assistant Professor of Mathematics

Bell Tower West, Room 2235

(805) 437-3122

geoffrey.buhl@csuci.edu

Geoffrey Dougherty , Ph.D.

Professor of Physics

Applied Physics Coordinator

Aliso Hall, Room 101

(805) 437-8990

geoff.dougherty@csuci.edu

Jesse Elliott, Ph.D.

Assistant Professor of Mathematics

Bell Tower West, Room 2215

(805) 437-2768

jesse.elliott@csuci.edu

Jorge Garcia, Ph.D.

Assistant Professor of Mathematics

Developmental Mathematics Coordinator

Bell Tower West, Room 2219

(805) 437-2769

jorge.garcia@csuci.edu

Kathryn Leonard , Ph.D.

Assistant Professor of Mathematics

Bell Tower West, Room 2245

(805) 437-3127

kathryn.leonard@csuci.edu

Gregory Wood, Ph.D.

Assistant Professor of Physics

Bell Tower West, Room 2295

(805) 437-3279

gregory.wood@csuci.edu

Cindy Wyels, Ph.D.

Associate Professor of Mathematics

MS in Mathematics Graduate Program Director

Bell Tower West, Room 1191

(805) 437-3260

cynthia.wyels@csuci.edu

## Contact Information

## Requirements For The Bachelor of Science In Mathematics (120 units)

### Lower Division Requirements (34-35 units)

MATH 150 Calculus I (4)

MATH 151 Calculus II (4)

MATH 230 Logic and Mathematical Reasoning (3)

MATH 240 Linear Algebra (3)

MATH 250 Calculus III (3)

PHYS 200 General Physics I (4)

*Select one of the following:*

PHYS 201 and one additional science course (7-8)

One two-semester science sequence (7-8)

*Select one of the following:*

COMP 105 Computer Programming Introduction (4)

COMP 150 Object Oriented Programming (4)

*Select an additional Computer Science course:*

COMP 102 **or** above (2-4)

### Upper Division Requirements (20 units)

MATH 300 Discrete Mathematics (3)

MATH 331 History of Mathematics (3)

MATH 350 Differential Equations and Dynamical Systems (3)

MATH 351 Real Analysis (3)

MATH 352 Probability and Statistics (3)

MATH 451 Complex Analysis (3)

MATH 499 Senior Colloquium (1) (twice)

### Electives in Major (9-13 units)

**Note:**

- Courses used for the emphases cannot be counted
as elective.

- Students planning on teaching math have to choose

MATH 492 for field experience requirement. Other courses recommended for teaching careers are marked with T.

MATH 318 Mathematics for Secondary School Teachers (3 - T)

MATH 330 Mathematics and Fine Arts (3 - T)

MATH 345 Digital Image Processing (PHYS) (3)

MATH 354 Analysis of Algorithms (3)

MATH 393 Abstract Algebra (3 -T)

MATH 429 Operations Research (3)

MATH 430 Research Design and Data Analysis (3)

MATH 437 Mathematics for Game Development (3)

MATH 445 Image Analysis and Pattern Recognition (PHYS) (3)

MATH 448 Scientific Computing (3)

MATH 450 Partial Differential Equations and Mathematical Physics (3)

MATH 452 Computational Bioinformatics (COMP) (3)

MATH 480 Differential & Riemannian Geometry (3)

MATH 482 Number Theory and Cryptography (3 - T)

MATH 484 Algebraic Geometry and Coding Theory (3)

MATH 490 Topics in Mathematics (3)

MATH 492 Internship (3 - T - required)

MATH 494 Independent Study (3)

MATH 497 Directed Study (3)

MATH 499 Senior Colloquium (1)

### Required Supporting and Other GE Courses

GE and American Institutions Requirement (34 units)

Elective Courses (16 units)

*Select one interdisciplinary GE Course (3 units)*

**Recommended:**

COMP 447 Societal Issues in Computing (3)

COMP 449 Human Computer Interactions (PSY) (3)

PHYS 434 Introduction to Biomedical Imaging (BIOL/HLTH) (4)

#### Emphasis (6-10 units)

By the sophomore year, in order to plan their electives, students should decide on
one of the following emphases and take all courses listed in the section.

#### Biomathematics (10 units)

*Students selecting this emphasis should take BIOL 201*

MATH 202 Biostatistics (PSY) (3)

MATH 430 Research design and Data Analysis (3)

MATH 452 Computational Bioinformatics (COMP) (4)

#### Computer Science (9 units)

*Students selecting this emphasis should take COMP 150 and COMP 151 for the computer
science requirements*

MATH 448 Scientific Computing (3)

MATH 354 Analysis of Algorithms (3)

COMP 350 Introduction to Software Engineering (3)

#### Physics (6 units)

*Students selecting this emphasis should take PHYS 200 and 201(8) as the science sequence.*

MATH 450 Partial Differential Equations and Mathematical Physics (3)

Upper division Physics course (3)

#### Applied Physics (6 units)

*Students selecting this emphasis should take PHYS 200 and 201(8) as the science sequence*

COMP 345 Digital Image Processing (PHYS) (3)

COMP 445 Image Analysis and Pattern
Recognition (PHYS) (3)

#### Actuarial Sciences/Economics (9 units)

MATH 429 Operations Research (3)

ECON 300 Fundamentals of Economics (3)

ECON 486 Introduction to Econometrics (3)

#### Business Management (9 units)

MATH 329 Statistics for Business and Economics (3)

MATH 429 Operations Research (3)

Economics **or** Upper Division Management Course (3)

#### Cognitive Science (9 units)

MATH 430 Research Design and Data Analysis (3)

PSY 210 Learning, Cognition and Development (3)

Upper Division Cognitive Psychology Course (3)

#### Education (9 units)

MATH 318 Mathematics for Secondary School Teachers (3)

MATH 393 Abstract Algebra I (3)

EDUC 512 Equity, Diversity and Foundations of Schooling (3)

#### Applied Mathematics (9 units)

MATH 429 Operations Research (3)

MATH 448 Scientific Computing (3)

MATH 450 Partial Differential Equations and Mathematical Physics (3)

#### Digital Design (9 units)

MATH 393 Abstract Algebra (3)

ART 108 Visual Technologies (3)

*Select one of the following:*

ART 312 Digital Media Art: Time-Based Imaging and Compositing (3)

ART 314 Digital Media Art: Digital Photography (3)

*Choice of other emphases or individualized emphasis is possible upon approval of the mathematics advisor.*

### Proposed Course of Study

#### Freshman Year (30-32 units)

MATH 150 Calculus I (4) GE B3

MATH 151 Calculus II (4)

MATH 230 Logic and Mathematical Reasoning
(3) GE A3

MATH 399 Modern Tech in Math (1) (twice)

PHYS 200 General Physics I (4) GE B2

Computer Science Course (2-4)

GE Section A, C, D, or E (3)

*Select one of the following:*

COMP 105 Computer Programming Introduction (3-4) GE B4

COMP 150 Object Oriented Programming (4) GE B4

*Select either (ENGL 102+103) or ENGL 105*

ENGL 102 Stretch Composition I (3)

ENGL 103 Stretch Composition II (3)

**or**

ENGL 105 Composition and Rhetoric (3) GE A2

#### Sophomore Year (22-23 units)

MATH 240 Linear Algebra (3)

MATH 250 Calculus III (3)

MATH 300 Discrete Mathematics (3)

MATH 350 Differential Equations and Dynamical Systems (3)

MATH 399 Modern Tech in Math (1)

#### Junior Year (15-18 units + GE)

MATH 331 History of Mathematics (3) GE B3, D, INTD

MATH 351 Real Analysis (3)

MATH 352 Probability and Statistics (3)

*Choose one of the groups from the Emphasis Courses
listed above*

#### Senior Year (14-15 units + GE)

MATH 451 Complex Analysis (3)

MATH 499 Senior Colloquium (1) Fall

MATH 499 Senior Colloquium (1) Spring

*Choose three or more Math Electives (9-12)*

### Total Requirements for the Bachelor of Science in Mathematics Degree (120 units)

Lower Division Required Major Courses (34-35)

Upper Division Required Major Courses (20)

Upper Division Elective & Emphasis Major Courses (15-19)

Electives (16)

GE Included in Major Requirements (18)

GE and American Institutions Requirement (34)

**Total (120)**

## Requirements for the Minor in Mathematics (20 units)

MATH 150 Calculus I (4)

MATH 151 Calculus II (4)

MATH 300 Discrete Mathematics (3)

In addition, students should select three upper division courses (9 units) from the Mathematics program approved by the advisor. Approval is not required for Computer Science majors.

## Requirements for the Minor in Foundational Mathematics (34-36 units)

This minor meets the needs of non-mathematics majors intending to enter a middle school mathematics teaching credential program. Especially, many Liberal Studies students would like to teach upper level elementary mathematics.

### Lower Division Requirements (15-16 units)

**(including pre-/co-requisites)**

*Choose one of the following:*

MATH 101 College Algebra (3)

MATH 105 Pre-Calculus (4)

MATH 150 Calculus I (4)

*Choose one of the following:*

MATH 201 Elementary Statistics (3)

MATH 202 Biostatistics (3)

*Additional required courses:*

MATH 208 Modern Mathematics for Elementary Teaching I-Numbers and Problem Solving
(3)

MATH 230 Logic & Mathematical Reasoning (3)

MATH 240 Linear Algebra (3)

### Upper Division Requirements (16 units)

**(including pre-/co-requisites)**

MATH 308 Modern Mathematics for Elementary School Teaching II-Geometry, Probability
and Statistics (3)

MATH 318 Mathematics for Secondary School Teachers (3-T) (3)

MATH 330 Mathematics and Fine Arts (3)

MATH 331 History of Mathematics (3)

MATH 499 Senior Colloquium (1)

*Select one of the following:*

MATH 492 Internship (1-3)

LS 499 Capstone Project (1-3)

#### Electives

*Choose one course from the list below (3-4 units)*

MATH 150 Calculus I (4)

MATH 151 Calculus II (4)

MATH 300 Discrete Mathematics (3)

MATH 393 Abstract Algebra I (3)

MATH 482 Number Theory & Cryptography (3)

**or**

Other upper division math course (3-4)

## Master of Science in Mathematics

(Offered through CSU Channel Islands’ Extended Education Program)

Our MS in Mathematics program is interdisciplinary and innovative in nature, and offers a flexible schedule with highly qualified faculty. It is designed to address the global need for people with advanced mathematical, computational, and computer skills throughout the industry, high-tech, and educational systems. Students will be given a strong background in mathematics, and computer software, as well as the skills to conduct independent applied research or develop independent projects. The program will stress interdisciplinary applications, for example in Actuarial Sciences, Cryptography, Security, Image Recognition, Artificial Intelligence, and Mathematics Education. Students’ specializations depend on the final project/ thesis and the electives chosen under the supervision of Mathematics advisor. An individual study plan can be designed to meet entry requirements for Ph.D. programs in Mathematical Sciences.

### Admission Requirements

**Application.**Apply to both the University and the

Mathematics Program. Forms are available at the Extended Education Office and on-line at http://math.csuci.edu/.

**Recommendation.**At least two letters of recommendations from academia or professional supervisors.

**Subject Matter Preparation**. Applicants are expected to hold BS degree in mathematics. However students with other degrees (or equivalent coursework) maybe considered and admitted conditionally (subject to completing relevant undergraduate mathematics courses).

**GPA of 3.0 in Mathematical Sciences.**If applicant does not have the required GPA, conditional admission maybe available on a limited bases.

**GRE**(general and mathematics) scores are recommended, but not required.

### Faculty and Contact Information

Cindy Wyels, Ph.D.

Associate Professor of Mathematics

MS in Mathematics Graduate Program Director

Bell Tower West, Room 1191

(805) 437-3260

cynthia.wyels@csuci.edu

Ivona Grzegorczyk, Ph.D.

Professor of Mathematics and

Chair, Mathematics Program

Bell Tower West, Room 2275

(805) 437-8868

ivona.grze@csuci.edu

### Requirements for the Master of Science in Mathematics (32 units)

#### Core Courses (11 Units)

*Choose three courses from the following list:*

MATH 510 Probabilistic Methods and Measure Theory (3)

MATH 511 Functional Analysis (3)

MATH 513 Advanced Algebra (3)

COMP 510 Algorithms (3)

COMP 569 Artificial Intelligence (3)

PHYS 510 Advanced Image Analysis Techniques (3)

*And required two units of:*

MATH 599 Graduate Seminar (1)

#### Electives (15 Units)*

*Choose five electives from the following list (at least three courses in mathematics):*

MATH 511 Functional Analysis (3)

MATH 513 Advanced Algebra (3)

MATH 555 Actuarial Sciences (3)

MATH 565 Research in Mathematics Education (3)

MATH 581 Mathematical Methods in Artificial Intelligence (COMP) (3)

MATH 582 Number Theory and Cryptography (3)

MATH 584 Algebraic Geometry and Coding Theory (3)

MATH 587 Markov Chains and Markov Processes (3)

MATH 588 Stochastic Analysis (3)

PHYS 546 Pattern Recognition (3)

COMP 520 Advanced Database Systems (3)

COMP 524 Security (3)

COMP 529 Network Computing (3)

COMP 549 Human-Computer Interaction (3)

COMP 550 Advanced Software Engineering (3)

COMP 569 Artificial Intelligence (3)

COMP 571 Biologically Inspired Computing (3)

COMP 572 Neural Networks (3)

COMP 575 Multi-Agent Systems (3)

COMP 578 Data Mining (3)

*other graduate or junior/senior courses from related disciplines may be included with advisors approval.

### Projects or Masters Thesis Emphasis (6 units)

MATH 597 Master Thesis

**or**

MATH 598 Master Project

### Graduate Writing Assessment Requirement

Writing proficiency prior to the awarding of the degree is demonstrated by successful completion of at least two credits of MATH 597 (Masters Thesis) or MATH 598 (Masters Project) with a grade of B or higher.