## Mathematics

http://www.pacific.edu/Academics/Schools-and-Colleges/College-of-the-Pacific/Academics/Departments-and-Programs/Mathematics.html

Phone: (209) 946-2347

Location: Main Office in CR 106

Larry Langley, Chair

## Degrees Offered

**Bachelor of Arts
Bachelor of Science**

## Majors Offered

**Mathematics **(BA, BS)

**Mathematics with Departmental Honors** (BS)

**Applied Mathematics** (BS)

**Applied Mathematics with Departmental Honors** (BS)

## Minors Offered

**Mathematics
Applied Mathematics
Statistics**

The Mathematics Department shares the University mission of providing a superior, student-centered education. Education in mathematics assists students in developing, to their fullest potential, their mathematical reasoning, communication and problem solving skills. Students who choose to major in mathematics are provided opportunities to develop strong problem solving skills that use quantitative methods and appropriate technology. They understand the strengths, limitations and wide applicability of mathematical modeling in a variety of disciplines. Students develop an appreciation for the discipline and esthetics of mathematics, effectiveness in problem solving, and an appropriate understanding of theory. Graduates who major in mathematics are prepared for the many careers in which mathematics plays an important role, for further study in Mathematics at the graduate level, or for careers in teaching mathematics.

Students who prepare for careers in mathematics, mathematics teaching, or for graduate study in mathematics elect the Bachelor of Science degree. Students interested in applied areas or majoring in a discipline which uses mathematics elect the Bachelor of Science in Applied Mathematics. Students interested in mathematics primarily as a component of a liberal education or as a second major may elect the Bachelor of Arts degree. Minors in Mathematics, Applied Mathematics and Statistics are available to students who wish to add this component to their college experience. Students who choose to double major or minor in mathematics or who choose to study mathematics as part of their liberal arts education learn the major methods, applicability, and spirit of the mathematical sciences.

The Department of Mathematics also provides courses offering opportunities for students from other disciplines and professional programs to develop the quantitative skills necessary for success in their chosen field.

## Preparation for Studying Mathematics

Since many degree programs within the University require courses in mathematics, students are encouraged to complete four years of high school mathematics. In general this would include two years of algebra, a year of geometry and a year of Math Analysis that includes Trigonometry. Four years of IMP or CPM mathematics are usually equivalent to these traditional courses. Students with Advanced Placement AB credit (score of 4 or 5) or Math IB Higher Level (score of 5, 6, or 7) start college mathematics in Calculus II while students with AP BC credit (score of 4 or 5) start in Calculus III. AP credit in Statistics (score of 4 or 5) is equivalent to MATH 037. All students are tested for quantitative skills during student orientation sessions. A quantitative fundamental skills requirement is part of the general education program and requires passing an Intermediate Algebra or higher level test during orientation or completing a college level Statistics or College Algebra course. In order to enroll in mathematics department courses numbered MATH 033, MATH 035, MATH 041, MATH 045, MATH 051, MATH 053, or MATH 161, students must take and pass a mathematics placement examination appropriate to the course prerequisite. Some courses in Economics, Chemistry, Physics, Computer Science, Psychology, the Educational Resource Center and Political Science also have mathematics placement requirements. Students choose the test level to be taken in consultation with their faculty advisor. All freshmen are tested. These tests include placement tests in Calculus for students who have had Calculus but do not have AP credit or do not know their AP score. The Calculus (Form E placement) test is for placement only and does not award credit for MATH 051. Subject material for the examinations and sample questions are available at the Educational Resource Center website.

For students who need additional preparation before entering introductory college mathematics courses, the Mathematics Lab of the Educational Resource Center in the Benerd School of Education offers developmental skill courses in the areas of fundamental mathematics, algebra and Trigonometry.

## Pre-Professional Education Courses for Single Subject Mathematics or Foundational-Level Mathematics

Students who plan to earn a degree and a teaching credential through the University of the Pacific simultaneously are required to take certain professional education courses during their undergraduate years. Contact Marilyn Draheim in the Benerd School of Education or Dennis Parker in the Mathematics Department for details about these course requirements.

## Departmental Honors

The honors programs in mathematics and applied mathematics gives students the chance to work with a faculty supervisor on an advanced project, possibly related to current research in mathematics. It is ideal preparation for students interested in graduate study in math, applied math or a related field.

In order to be admitted into the Mathematics with Departmental Honors program, students must have a major GAP of at least 3.5, have completed MATH 049, and have completed or currently enrolled in two of the following: MATH 141, MATH 143, or MATH 155. In order to be admitted into the Applied Mathematics with Departmental Honors program, students must have a major GPA of at least 3.5, have completed MATH 055 and have completed or be currently enrolled in MATH 145. Junior or Senior class standing is recommended.

Students meeting the eligibility requirements may apply to graduate with Honors any time prior to the start of their final two semesters. To apply, a student must obtain the consent of a mathematics faculty member who is willing to supervise an honors project (typically completed during the student's senior year) and submit an application form to the Department Chair. *Once approved, a Change of Program form must be submitted to the Office of the Registrar.*

## Preparation for the Major

The first course in all Mathematics majors is Calculus I, II or III depending on the student’s high school preparation in mathematics. Majors with AP Math AB or IB Math HL credit start in Calculus II. Majors with AP Math BC credit start in Calculus III. Students who are not able to start in Calculus I because of deficiencies in their algebra or Trig skills start in MATH 041, Precalculus. Students who place lower than MATH 041 discuss with their advisor how much extra time is required to complete their degree program because of the required developmental work. Mathematics majors are proficient with graphing calculators and consider taking elective courses that use quantitative skills in areas such as business, economics, computer science, science and engineering.

## Bachelor of Arts Major in Mathematics

Students must complete a minimum of 124 units with a Pacific cumulative and major/program grade point average of 2.0 in order to earn the bachelor of arts degree with a major in mathematics.

### I. General Education Requirements

Minimum 42 units and 12 courses that include:

PACS 001 | What is a Good Society | 4 |

PACS 002 | Topical Seminar on a Good Society | 4 |

PACS 003 | What is an Ethical Life? | 3 |

* Note: 1) Pacific Seminars cannot be taken for Pass/No Credit. 2) Transfer students with 28 or more transfer units complete 2 additional General Education elective courses from below in place of taking *PACS 001

*and*PACS 002

*.*

One course from each subdivision below:

Social and Behavioral Sciences | ||

Arts and Humanities | ||

Natural Sciences and Mathematics | ||

or a second IIIA Natural Sciences course |

**Note:** **1****)** No more than 2 courses from a single discipline may be applied to meet the requirements of the general education program.

### II. Diversity Requirement

Students must complete one diversity course (3-4 units) |

**Note:** **1****)** Transfer students with 28 units or more transfer units prior to fall 2011 are encouraged but not required to complete a designated course prior to graduation. **2)** Courses may be used also to meet general education and/or major/minor requirements.

### III. College of the Pacific BA Requirement

Students must complete one year of college instruction or equivalent training in a language other than English.

*Note:**Transfer students with sophomore standing are exempt from this requirement.*

### IV. Fundamental Skills

Students must demonstrate competence in:

Writing | ||

Quantitative analysis |

### V. Breadth Requirement

Students complete 64 units outside the primary discipline of the first major, regardless of the department who offers the course(s) in that discipline. (This includes general education courses, transfer courses, CPCE/EXTN units, internships, etc.)

### VI. Major Requirements

Minimum 36 units and 10 courses that include:

MATH 049 | Introduction to Abstract Mathematics | 4 |

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

Select one of the following: | 4 | |

Introduction to Statistics and Probability | ||

Probability and Mathematical Statistics I | ||

Select one of the following: | 4 | |

Linear Algebra | ||

Applied Linear Algebra | ||

Select one of the following: | 4 | |

Abstract Algebra I | ||

Real Analysis I | ||

Three MATH Electives (excluding MATH 005, MATH 033, MATH 035, MATH 041, MATH 045, MATH 161, and MATH 162) Minimum 3 units each. | 9-12 |

**Note:** Electives must be approved by a mathematics advisor.

## Bachelor of Science Major in Mathematics

Students must complete a minimum of 124 units with a Pacific cumulative and major/program grade point average of 2.0 in order to earn the bachelor of science degree with a major in mathematics.

### I. General Education Requirements

Minimum 42 units and 12 courses that include:

PACS 001 | What is a Good Society | 4 |

PACS 002 | Topical Seminar on a Good Society | 4 |

PACS 003 | What is an Ethical Life? | 3 |

* Note: 1) Pacific Seminars cannot be taken for Pass/No Credit. 2) Transfer students with 28 or more transfer units complete 2 additional General Education elective courses from below in place of taking *PACS 001

*and*PACS 002

*.*

One course from each subdivision below:

Social and Behavioral Sciences | ||

Arts and Humanities | ||

Natural Sciences and Mathematics | ||

or a second IIIA Natural Sciences course |

**Note:** **1****)** No more than 2 courses from a single discipline may be applied to meet the requirements of the general education program.

### II. Diversity Requirement

Students must complete one diversity course (3-4 units) |

**Note:** **1****)** Transfer students with 28 units or more transfer units prior to fall 2011 are encouraged but not required to complete a designated course prior to graduation. **2)** Courses may be used also to meet general education and/or major/minor requirements.

### III. Fundamental Skills

Students must demonstrate competence in:

Writing | ||

Quantitative analysis |

### IV. Breadth Requirement

Students complete 64 units outside the primary discipline of the first major, regardless of the department who offers the course(s) in that discipline. (This includes general education courses, transfer courses, CPCE/EXTN units, internships, etc.)

### V. Major Requirements

Minimum 46 units and 13 courses that include:

MATH 049 | Introduction to Abstract Mathematics | 4 |

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 055 | Calculus III | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

MATH 141 | Linear Algebra | 4 |

MATH 143 | Abstract Algebra I | 4 |

MATH 155 | Real Analysis I | 4 |

MATH Electives (Two courses with any number, excluding MATH 005, MATH 033, MATH 035, MATH 041, MATH 045, MATH 161 and MATH 162, minimum 3 units each) | 6-9 | |

MATH Upper Division Electives (Three courses numbered MATH 110 or higher excluding MATH 161, and MATH 162, minimum 3 units each) | 9-12 |

## Bachelor of Science Major in Mathematics with Departmental Honors

Students must complete a minimum of 124 units with a Pacific cumulative grade point average of 3.3 and major/program grade point average of 3.5 in order to earn the bachelor of science degree with a major in mathematics with departmental honors.

### I. General Education Requirements

Minimum 42 units and 12 courses that include:

PACS 001 | What is a Good Society | 4 |

PACS 002 | Topical Seminar on a Good Society | 4 |

PACS 003 | What is an Ethical Life? | 3 |

* Note: 1) Pacific Seminars cannot be taken for Pass/No Credit. 2) Transfer students with 28 or more transfer units complete 2 additional General Education elective courses from below in place of taking *PACS 001

*and*PACS 002

*.*

One course from each subdivision below:

Social and Behavioral Sciences | ||

Arts and Humanities | ||

Natural Sciences and Mathematics | ||

or a second IIIA Natural Sciences course |

**Note:** **1****)** No more than 2 courses from a single discipline may be applied to meet the requirements of the general education program.

### II. Diversity Requirement

Students must complete one diversity course (3-4 units) |

**Note:** **1****)** Transfer students with 28 units or more transfer units prior to fall 2011 are encouraged but not required to complete a designated course prior to graduation. **2)** Courses may be used also to meet general education and/or major/minor requirements.

### III. Fundamental Skills

Students must demonstrate competence in:

Writing | ||

Quantitative analysis |

### IV. Breadth Requirement

Students complete 64 units outside the primary discipline of the first major, regardless of the department who offers the course(s) in that discipline. (This includes general education courses, transfer courses, CPCE/EXTN units, internships, etc.)

### V. Major Requirements

Minimum 46 units and 13 courses that include:

MATH 049 | Introduction to Abstract Mathematics | 4 |

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 055 | Calculus III | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

MATH 141 | Linear Algebra | 4 |

MATH 143 | Abstract Algebra I | 4 |

MATH 155 | Real Analysis I | 4 |

MATH Electives (Two courses with any number, excluding MATH 005, MATH 033, MATH 035, MATH 041, MATH 045, MATH 161 and MATH 162, minimum 3 units each) | 6-9 | |

MATH Upper Division Electives (Three courses numbered MATH 110 or higher excluding MATH 161, and MATH 162, minimum 3 units each) | 9-12 | |

MATH 197 | Undergraduate Research ^{*} | 2-4 |

Honors Thesis ^{*} |

*Note: 1) **Two semesters of MATH 197 under the direction of their chosen faculty supervisor. The second semester may focus on writing the Honors Thesis.*

## CSET Preparation (Future High School Math Teachers)

Students who pursue a California mathematics or foundational-level mathematics single-subject teaching credential may elect either the BA or BS program. In addition to earning a degree, students must show subject matter competency by passing the CSET (California Subject Exams for Teachers) in mathematics. Contact the Mathematics Credential Coordinator, Dr. Dennis Parker at dparker@pacific.edu for additional credential requirements. Below are the recommended coursework options for the BA and the BS.

- BA for Single Subject Math with CSET (California Subject Exams for Teachers)

Core MATH 049 Introduction to Abstract Mathematics 4 MATH 051 Calculus I 4 MATH 053 Calculus II 4 MATH 055 Calculus III 4 MATH 141 Linear Algebra 4 MATH 143 Abstract Algebra I 4 Select one of the following Probability and Statistics course: 4 Introduction to Statistics and Probability Probability and Mathematical Statistics I Recommended Electives Topics in History of Mathematics Mathematical Concepts for Secondary Education Modern Geometries

- BS for Single Subject Math with CSET

Core MATH 049 Introduction to Abstract Mathematics 4 MATH 051 Calculus I 4 MATH 053 Calculus II 4 MATH 055 Calculus III 4 MATH 141 Linear Algebra 4 MATH 143 Abstract Algebra I 4 MATH 155 Real Analysis I 4 Recommended Electives Introduction to Statistics and Probability Operations Research Models Discrete and Combinatorial Mathematics Topics in History of Mathematics Mathematical Concepts for Secondary Education Modern Geometries

Students who do not major in mathematics, but wish to earn a California mathematics or foundational-level mathematics teaching credential, may consider earning a minor in mathematics to help prepare them for the CSET exams. Below are minor coursework options recommended for mathematics teacher preparation.

MATH 037 | Introduction to Statistics and Probability | 4 |

MATH 049 | Introduction to Abstract Mathematics | 4 |

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 141 | Linear Algebra | 4 |

MATH 166 | Mathematical Concepts for Secondary Education | 3 |

MATH 168 | Modern Geometries | 4 |

## Bachelor of Science Major in Applied Mathematics

Students must complete a minimum of 124 units with a Pacific cumulative and major/program grade point average of 2.0 in order to earn the bachelor of science degree with a major in applied mathematics.

### I. General Education Requirements

Minimum 42 units and 12 courses that include:

PACS 001 | What is a Good Society | 4 |

PACS 002 | Topical Seminar on a Good Society | 4 |

PACS 003 | What is an Ethical Life? | 3 |

**Note:** **1)** Pacific Seminars cannot be taken for Pass/No Credit. **2)** Transfer students with 28 or more transfer units complete 2 additional General Education elective courses from below in place of taking * and *PACS 002*.*

One course from each subdivision below:

Social and Behavioral Sciences | ||

Arts and Humanities | ||

Natural Sciences and Mathematics | ||

or a second IIIA Natural Sciences course |

**Note:** **1****)** No more than 2 courses from a single discipline may be applied to meet the requirements of the general education program.

### II. Diversity Requirement

Students must complete one diversity course (3-4 units) |

**Note:** **1****)** Transfer students with 28 units or more transfer units prior to fall 2011 are encouraged but not required to complete a designated course prior to graduation. **2)** Courses may be used also to meet general education and/or major/minor requirements.

### III. Fundamental Skills

Students must demonstrate competence in:

Writing | ||

Quantitative analysis |

### IV. Breadth Requirement

### V. Major Requirements

Minimum 44 units and 13 courses that include:

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 055 | Calculus III | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

MATH 145 | Applied Linear Algebra | 4 |

COMP 051 | Introduction to Computer Science | 4 |

Select one of the following: | 4 | |

Introduction to Abstract Mathematics | ||

Applied Differential Equations I: ODEs | ||

Select three of the following (minimum 3 units per course): | 9-12 | |

Introduction to Statistics and Probability | ||

Probability with Applications to Statistics | ||

Operations Research Models | ||

Discrete and Combinatorial Mathematics | ||

Numerical Analysis | ||

Financial Mathematics I | ||

Financial Mathematics II | ||

Topics in Applied Statistics | ||

Probability and Mathematical Statistics I | ||

Probability and Mathematical Statistics II | ||

Cryptography | ||

Vector Analysis | ||

Applied Differential Equations II | ||

Graph Theory | ||

MATH 193 Special Topics (to be approved by advisor) |

**Note:** **1)** Electives are to be chosen in consultation of a major advisor. **2) **At most one elective may be numbered lower than 110.** 3)** One elective may be chosen from the following experiences: independent study, undergraduate research, internship, and practicum.

Choose either 1 or 2, 8-12 units

- Students take three mathematically oriented courses from one or several of the mathematical sciences (e.g. Physics, Chemistry, Engineering, Computer Science, Economics, Management Sciences or other fields), chosen from a list of approved courses available in the mathematics department. In most cases, this requirement is fulfilled by courses required for the degree programs mentioned, with suitable electives.
- Students take two mathematically oriented courses from one of the several mathematical sciences, as described in (1), plus one MATH elective (at least 3 units) numbered MATH 049 or higher (excluding MATH 161, MATH 162, and MATH 166).

## Bachelor of Science Major in Applied Mathematics with Departmental Honors

Students must complete a minimum of 124 units with a Pacific cumulative grade point average of 3.3 and minimum major/program grade point average of 3.5 in order to earn the bachelor of science degree with a major in applied mathematics with departmental honors.

### I. General Education Requirements

Minimum 42 units and 12 courses that include:

PACS 001 | What is a Good Society | 4 |

PACS 002 | Topical Seminar on a Good Society | 4 |

PACS 003 | What is an Ethical Life? | 3 |

**Note:** **1)** Pacific Seminars cannot be taken for Pass/No Credit. **2)** Transfer students with 28 or more transfer units complete 2 additional General Education elective courses from below in place of taking * and *PACS 002*.*

One course from each subdivision below:

Social and Behavioral Sciences | ||

Arts and Humanities | ||

Natural Sciences and Mathematics | ||

or a second IIIA Natural Sciences course |

**Note:** **1****)** No more than 2 courses from a single discipline may be applied to meet the requirements of the general education program.

### II. Diversity Requirement

Students must complete one diversity course (3-4 units) |

**Note:** **1****)** Transfer students with 28 units or more transfer units prior to fall 2011 are encouraged but not required to complete a designated course prior to graduation. **2)** Courses may be used also to meet general education and/or major/minor requirements.

### III. Fundamental Skills

Students must demonstrate competence in:

Writing | ||

Quantitative analysis |

### IV. Breadth Requirement

### V. Major Requirements

Minimum 44 units and 13 courses that include:

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 055 | Calculus III | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

MATH 145 | Applied Linear Algebra | 4 |

COMP 051 | Introduction to Computer Science | 4 |

Select one of the following: | 4 | |

Introduction to Abstract Mathematics | ||

Applied Differential Equations I: ODEs | ||

Select three of the following (minimum 3 units per course): | 9-12 | |

Introduction to Statistics and Probability | ||

Probability with Applications to Statistics | ||

Operations Research Models | ||

Discrete and Combinatorial Mathematics | ||

Numerical Analysis | ||

Financial Mathematics I | ||

Financial Mathematics II | ||

Topics in Applied Statistics | ||

Probability and Mathematical Statistics I | ||

Probability and Mathematical Statistics II | ||

Cryptography | ||

Vector Analysis | ||

Applied Differential Equations II | ||

Graph Theory | ||

MATH 193 Special Topics (to be approved by advisor) | ||

MATH 197 | Undergraduate Research ^{*} | 2-4 |

Honors Thesis ^{*} |

**Note:** **Note:** **1)** Electives are to be chosen in consultation of a major advisor. **2) **At most one elective may be numbered lower than 110.** 3)** One elective may be chosen from the following experiences: independent study, undergraduate research, internship, and practicum. **4)** Two semesters of MATH 197 under the direction of their chosen faculty supervisor. The second semester may focus on writing the Honors Thesis.

Choose either 1 or 2, 8-12 units

- Students take three mathematically oriented courses from one or several of the mathematical sciences (e.g. Physics, Chemistry, Engineering, Computer Science, Economics, Management Sciences or other fields), chosen from a list of approved courses available in the mathematics department. In most cases, this requirement is fulfilled by courses required for the degree programs mentioned, with suitable electives.
- Students take two mathematically oriented courses from one of the several mathematical sciences, as described in (1), plus one MATH elective (at least 3 units) numbered MATH 049 or higher (excludingMATH 161, MATH 162, and MATH 166).

## Minors

The study of mathematics is a process that develops important modes of critical thinking. Because quantitative problem solving is a desirable skill, a minor in mathematics can be a beneficial addition to the program of any student at Pacific irrespective of his/her major. Mathematics minors may also benefit students who plan on further graduate education in related areas. Minors in mathematics are designed to offer a measure of breadth and some depth in the student’s mathematical experience. Only courses passed with a C- or better grade are used to meet the minor requirements. A minimum of 12 of the minor units must be completed at Pacific. Students who plan to minor in mathematics contact the chair of the Mathematics Department and are assigned a minor advisor.

## Minor in Mathematics

Students must complete a minimum of 23 units with a Pacific minor grade point average of 2.0 in order to earn a minor in Mathematics.

### Minor Requirements:

MATH 049 | Introduction to Abstract Mathematics | 4 |

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

Select one of the following: | 4 | |

Linear Algebra | ||

Abstract Algebra I | ||

Real Analysis I | ||

Select one MATH elective | 3-4 |

## Minor in Statistics

Students must complete a minimum of 25 units with a Pacific minor grade point average of 2.0 in order to earn a minor in statistics.

### Minor Requirements:

Select one of the following: | 4 | |

Elementary Statistical Inference | ||

Introduction to Statistics and Probability | ||

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 130 | Topics in Applied Statistics | 3 |

MATH 131 | Probability and Mathematical Statistics I | 4 |

Two additional courses relevant to statistics (at least 3 units each) | 6-8 |

**Note:** Electives are to be chosen in consultation of a minor advisor.

## Minor in Applied Mathematics

Students must complete a minimum of 20 units with a Pacific minor grade point average of 2.0 in order to earn a minor in applied mathematics.

### Minor Requirements:

MATH 051 | Calculus I | 4 |

MATH 053 | Calculus II | 4 |

MATH 075 | Introduction to Linear Algebra | 4 |

MATH 145 | Applied Linear Algebra | 4 |

Three MATH Electives (see notes below) | 9-12 |

*Note: ** 1) Electives are to be chosen in consultation of a minor advisor. 2) Units earned for *MATH 033

*,*MATH 035

*,*MATH 037

*,*MATH 039

*,*MATH 041

*,*MATH 045

*,*MATH 161

*, or*MATH 162

*do not count as elective units toward the minor in applied mathematics.*

### Mathematics Courses

**MATH 001. Pre-algebra and Lab. 3 Units.**

This course is designed for students whose Mathematics Placement Test score indicates a need to review arithmetic skills and Pre-algebra material. Topics covered include fractions, decimals, percents, basic area and volume formulas, signed numbers, use of variables in mathematical statements, translating statements in English to mathematical equations, solving linear equations and ratio and proportion. The course is taught using a Personalized System of Instruction. Neither the course credit nor course grade applies towards graduation. Prerequisite is an appropriate test score or permission of instructor.

**MATH 003. Elementary Algebra and Lab. 3 Units.**

Topics covered include signed numbers, linear equations, polynomials, factoring, algebraic fractions, radicals, quadratic equations, inequalities and systems of linear equations. This is an introductory course for students with limited high school background in mathematics. This course is taught using a Personalized System of Instruction. This course is inappropriate for students who have passed the Elementary Algebra placement exam or any higher level placement exam. Neither the course credit nor course grade applies towards graduation. Prerequisite: MATH 001 with a "C" or better or an appropriate test score or permission of instructor.

**MATH 005. Intermediate College Algebra. 3 Units.**

This course is taught in a traditional lecture format. Topics covered in this course include the real number system, solution of linear equations and inequalities, word problems, factoring, algebraic equations, exponents and radicals, quadratic equations, relations, functions, graphs, systems of equations and logarithmic and exponential functions. This course is not appropriate for students who have passed the Intermediate Algebra placement test of any higher level test. Pass/No Credit (P/NC) grading option is not allowed for this course. A grade of C- or better is required to satisfy the University’s Fundamental Skills requirement in quantitative analysis/math. Prerequisite: MATH 003 with a “C-“ or better or an appropriate test score or permission of instructor. **(MATH)**

**MATH 005E. Intermediate College Algebra and Lab. 3 Units.**

This course is taught using the emporium model in which students use technology to drive their learning in a lab setting with on-demand support from the instructor and tutors. Topics covered in this course include the real number system, solution of linear equations and inequalities, word problems, factoring, algebraic equations, exponents and radicals, quadratic equations, relations, functions, graphs, systems of equations and logarithmic and exponential functions. This course is not appropriate for students who have passed the Intermediate Algebra placement test of any higher level test. Pass/No Credit (P/NC) grading option is not allowed for this course. A grade of C- or better is required to satisfy the University’s Fundamental Skills requirement in quantitative analysis/math. Prerequisite: MATH 003 with a “C-“ or better or an appropriate test score or permission of instructor. **(MATH)**

**MATH 007. Trigonometry and Lab. 2 Units.**

Topics in this course include angle measure, trigonometric functions, applications of trigonometry, graphs of trigonometric functions, trigonometric identities, inverse functions and complex numbers. This course is designed for students who have not studied trigonometry in high school. Prerequisites include a satisfactory score on the Intermediate Algebra placement test. This course is taught using a Personalized System of Instruction and meets three hours per week. Pass/No credit (P/NC) grading option is not allowed for this course. Students who complete MATH 005 and MATH 007 with a C- or better may enroll in MATH 051. Prerequisite: MATH 005 with a "C-" or better, an appropriate test score, or permission of instructor. **(MATH)**

**MATH 033. Elements of Calculus. 4 Units.**

This course covers polynomial, rational, exponential and logarithmic functions as well as differentiation, integration and maxima/minima of functions of several variables. Elementary differential equations are studied and applications to natural sciences, social sciences and other fields are covered. Credit is not given for this course if a students has received credit for MATH 051 or AP credit in Calculus. Prerequisites: Two years of high school algebra and an appropriate score on either the Intermediate Algebra placement test or the Pre-Calculus placement test; or MATH 005 or MATH 041 with a "C-" or better. **(GE3B, MATH)**

**MATH 035. Elementary Statistical Inference. 4 Units.**

Emphasis is on the applications and limitations of statistical methods of inference, especially in the social and behavioral sciences. Topics include: estimation and test of hypothesis concerning a signel group, One-way Analysis of Variance and analysis of categorical data. The use of statistical computer programs is addressed. Credit is not given for this course if a student has received credit for MATH 037 or has AP credit in Statistics. Prerequisite: MATH 003 or MATH 005 or MATH 041 with a "C-" or better, or an appropriate score on either the Elementary Algebra placement test, the Intermediate Algebra Placement test, or the Pre-calculus placement test or permission of instructor. **(ENST, GE3B, MATH, PLAW)**

**MATH 037. Introduction to Statistics and Probability. 4 Units.**

Students study elements of descriptive statistics: graphs, tables, measures of central tendency and dispersion. Probability models including binomial and normal are covered. The course introduces to estimation, hypothesis testing and analysis of variance in addition to linear and multiple regression and correlation. The use of statistical computer programs is addressed. The course is not recommended for first semester freshmen. Credit is not given for this course if a student has received credit for MATH 035 or has AP credit in Statistics. Prerequisites: MATH 033 or MATH 041 or MATH 045 or MATH 051 or MATH 053 with a "C-" or better or appropriate score on the calculus placement test. **(ENST, GE3B, MATH, PLAW)**

**MATH 039. Probability with Applications to Statistics. 4 Units.**

Probability concepts in discrete and continuous spaces is explored in some depth as well as important probability models (e.g., binomial, Poisson, exponential, normal, etc.), mathematical expectation and generating functions. Applications to statistical inference includes maximum likelihood, moment and least squares estimation. Confidence intervals and hypothesis testing is also covered. Credit is not given for both MATH 039 and MATH 131. Prerequisite: MATH 053 with a "C-" or better. **(GE3B)**

**MATH 041. Pre-calculus. 4 Units.**

The algebraic and trigonometric concepts which are necessary preparation for Calculus I are studied. Topics include the real number system, algebraic, trigonometric, exponential and logarithmic functions. Emphasis is on the function concept; graphing functions; solving equations, inequalities and linear systems; and applied problems. Credit for this course is not given if a student has AP Calculus credit. Prerequisite: MATH 005 with a "C-" or better or an appropriate score on either the Intermediate Algebra placement test, the Pre-calculus placement test or the calculus placement test. **(GE3B, MATH)**

**MATH 045. Introduction to Finite Mathematics and Calculus. 4 Units.**

This course introduces calculus, applications to problems in economics, management and other fields. Students study systems of equations, elements of matrix algebra, and elementary linear programming. Credit for this course is not given if a student has credit for MATH 051 or AP Calculus credit. Prerequisites: two years of high school Algebra and an appropriate score on either the Intermediate Algebra placement test, the Pre-calculus placement test, or the Calculus placement test; or MATH 005 or MATH 041 with a "C-" or better. **(GE3B, MATH)**

**MATH 049. Introduction to Abstract Mathematics. 4 Units.**

An introduction to the spirit and rigor of mathematics is the focus of the course. The content may vary with instructor, but the objective is to develop the skills required to read and write mathematics and prove theorems. Concepts include elementary logic, sets and functions, cardinality, direct and indirect proofs, mathematical induction. Prerequisite: MATH 053 with a "C-" or better or permission of the instructor.

**MATH 051. Calculus I. 4 Units.**

Students study differential calculus of algebraic and elementary transcendental functions, anti-derivatives, introductory definite integrals, and the Fundamental Theorem of Calculus. Applications, include the first and second derivative tests and optimization. Students who earn AP Math AB credit do not receive credit for MATH 051. Prerequisites: MATH 007 or MATH 041 with a "C-" or better or four years of high school mathematics including Trigonometry and an appropriate score on the placement test for calculus. **(GE3B, MATH)**

**MATH 052. A Calculus Companion. 1 Unit.**

An introduction to the foundations of calculus. This course provides a deeper look into the inner workings, formalities, history, and mysteries of Calculus. Foundations of the real numbers from axiomatic and set-theoretic perspectives. Number systems: real numbers, rationals, irrationals, integers, natural numbers, complex numbers. Cardinal numbers, Functions. The formal definition of the limit. Continuity and differentiability. Why the tangent line is the best linear approximation. A brief history of the differential. The theorems of calculus: Intermediate Value Theorem, Mean Value Theorem, Extreme Value Theorem, The Fundamental Theorem of Calculus, et al. Prerequisite may be taken concurrently: MATH 051.

**MATH 053. Calculus II. 4 Units.**

This course covers techniques and applications of integration, sequences and series, convergence of series, and Taylor Polynomials. Students who earn AP Math BC credit do not receive credit for MATH 053. Prerequisite: MATH 051 with a "C-" or better or an appropriate score on the calculus placement test. **(GE3B, MATH)**

**MATH 055. Calculus III. 4 Units.**

This course introduces multivariable calculus. Topics covered include vector geometry of the plane and Euclidean 3-space; differential calculus of real-valued functions of several variables, as well as partial derivatives, gradient, max-min theory, quadratic surfaces, and multiple integrals. Prerequisite: MATH 053 with a "C-" or better or AP Math BC credit. **(GE3B)**

**MATH 057. Applied Differential Equations I: ODEs. 4 Units.**

Students study ordinary differential equations, first-order equations, separable and linear equations. Also covered are direction fields, second order linear equations with constant coefficients, method of undetermined coefficients, laplace transforms, and unit impulse response and convolutions. Homogeneous systems of first order linear equations and matrix algebra determinants, eigenvalues, eigenvectors are also studied. Existence and uniqueness theorems are discussed and calculators or computers are used to display solutions and applications. Prerequisite: MATH 055 with a "C-" or better or permission of instructor.

**MATH 072. Operations Research Models. 4 Units.**

Operations Research (OR) is concerned with scientific design and operation of systems which involve the allocation of scarce resources. This course surveys some of the quantitative techniques used in OR. Linear Programs are solved using graphical techniques and the simplex algorithm. Among the other models studied is the transportation, assignment, matching, and knapsack problems. Prerequisite: MATH 033 or MATH 045 or MATH 051 with a "C-" or better or the appropriate score on the calculus placement test. **(GE3B)**

**MATH 074. Discrete and Combinatorial Mathematics. 4 Units.**

The fundamental principles of discrete and combinatorial mathematics are covered. Topics include the fundamental principles of counting, the Binomial Theorem, generating functions, recurrence relations and introductory graph theory, that includes trees and connectivity. Prerequisite: MATH 033 or MATH 045 or MATH 051 with a "C-" or better, or an appropriate score on the calculus placement test.

**MATH 075. Introduction to Linear Algebra. 4 Units.**

Linear algebra is the generalized study of solutions to systems of linear equations. The study of such systems dates back over 2000 years and now is foundational in the design of computational algorithms for many modern applications. This course will serve as an introduction to basic computational tools in linear algebra including the algebra and geometry of vectors, solutions to systems of linear equations, matrix algebra, linear transformations, determinants, eigenvalue-eigenvector problems, and orthogonal bases. Prerequisite: MATH 051 with a “C-“ or better.

**MATH 081. Writing Math Problems. 1 Unit.**

This course is an introduction to LaTeX math typesetting software commonly used by mathematicians including document creation, special document classes, mathematics commands and terminology. Writing problems for contests in multiple content areas and proofreading math problems. Practicum aspect: students will provide the content and grading for Pacific’s Avinash Raina High School Math Competition. Prerequisite may be taken concurrently: MATH 051. (Spring).

**MATH 093. Special Topics. 1-4 Units.**

**MATH 095. Problem Solving Seminar. 1 Unit.**

The objective of this course is to learn mathematics through problem solving. Students in mathematics courses are often given the impression that to solve a problem, one must imitate the solution to a similar problem that has already been solved. This course will attempt to develop student creativity in solving problems by considering problems not commonly encountered in other mathematics courses. Students enrolled in this course are expected to participate in the William Lowell Putnam Mathematical Competition on the first Saturday in December. Students may take this course for credit at most four times. Prerequisite: MATH 053 with a "C-" or better.

**MATH 110. Numerical Analysis. 4 Units.**

Numerical analysis deals with approximation of solutions to problems arising from the use of mathematics. The course begins with a necessary but brief discussion of floating point arithmetic, and then proceeds to discuss the computer solution of linear algebraic systems by elimination and iterative methods, the algebraic eigenvalue problem, interpolation, numeric integration, that includes a discussion of adaptive quadrature, the computation of roots of nonlinear equations and the numerical solution of initial value problems in ordinary differential equations. Prerequisite: MATH 055 with a "C-" or better.

**MATH 121. Financial Mathematics I. 4 Units.**

This course is designed to prepare students for Society of Actuaries Financial Mathematics examination and provides understanding of fundamental concepts of financial mathematics. Topics include interest rates, annuities, with level and varying payments, non-annual interest rates and annuities, projects appraisal and loans, term structure of interest rates, duration, convexity, and Immunization. This course covers about 60-65% of the topics on Exam FM. Prerequisite: MATH 053 or permission of instructor.

**MATH 122. Financial Mathematics II. 4 Units.**

The course is to provide an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The students will also be given an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics. This course consists of two parts. Part I covers the Financial Economics portion (about 40%) of the topics listed on Exam FM syllabus. Topics include the term structure of interest rates, cash flow matching, immunization (including full immunization), Redington immunization, general derivative markets, arbitrage-free model, options, forwards and future contracts, swaps, hedging and investment strategies. Part II serves as a preparation/review for the actuarial Exam FM. Prerequisite: MATH 121.

**MATH 130. Topics in Applied Statistics. 3 Units.**

This course covers topics in applied statistics not normally covered in an introductory course. Students study multiple regression and correlation, analysis of variance of one- and two-way designs and other topics selected from non-parametric methods, time series analysis, discriminant analysis, factor analysis, that depend upon student interest. There is extensive use of packaged computer programs. Prerequisites: MATH 035 or MATH 037 with a "C-" or better.

**MATH 131. Probability and Mathematical Statistics I. 4 Units.**

This course covers counting techniques, discrete and continuous random variables, distribution functions, special probability densities such as binomial, hypergeometric, geometric, negative binomial, Poisson, Uniform, Gamma, Exponential, Weibull, and Normal. Students study joint distributions, marginal and conditional distributions, mathematical expectations, moment generating functions, functions of random variables, sampling distribution of the mean, and the Central Limit Theorem. Credit is not given for both MATH 039 and MATH 131. Prerequisite: MATH 053 with a "C-" or better.

**MATH 132. Probability and Mathematical Statistics II. 4 Units.**

Sampling distributions such as Chi-square, t and F are studied as estimation methods such as methods of moments, maximum likelihood and least squares. The course covers properties of estimators such as unbiasedness, consistency, sufficiency, tests of hypothesis concerning means, difference between means, variances, proportions, one and two-way analysis of variance. Prerequisite: MATH 131 with a "C-" or better.

**MATH 141. Linear Algebra. 4 Units.**

Fundamental linear algebra concepts from an abstract viewpoint, with the objective of learning the theory and writing proofs. Concepts include: vector spaces, bases, linear transformations, matrices, invertibility, eigenvalues, eigenvectors, invariant subspaces, inner product spaces, orthogonality, and the spectral theorem. Prerequisites: MATH 049, MATH 075 with a "C-" or better.

**MATH 143. Abstract Algebra I. 4 Units.**

This is an introductory course to groups, rings and fields, with an emphasis on number theory and group theory. Students study finite groups, permutation groups, cyclic groups, factor groups, homomorphisms, and the isomorphic theorem. The course concludes with an introduction to polynomial rings. Prerequisite: MATH 049 with a "C-" or better or permission instructor.

**MATH 144. Abstract Algebra II. 4 Units.**

This course is a continuation of MATH 143, and it emphasizes field theory and the application of groups to geometry and field extensions. Students study algebraic and separable field extensions, dimension, splitting fields, Galois theory, solvability by radicals, and geometric constructions. Prerequisite: MATH 143 with a "C-" or better or permission of instructor.

**MATH 145. Applied Linear Algebra. 4 Units.**

This is the second semester course in linear algebra with an emphasis on the theory and application of matrix decompositions. Topics include methods for solving systems of equations, QR factorization, the method of least squares, diagonalization of symmetric matrices, singular value decomposition, and applications. Prerequisites: MATH 053, MATH 075 with a “C-“ or better.

**MATH 148. Cryptography. 3 Units.**

Cryptography and cryptanalysis from historical cryptosystems through the modern use of cryptology in computing are studied. Topics include public and symmetric key cryptosystems, digital signatures, modular arithmetic and other topics in number theory and algebra. Possible additional topics include error correcting codes, digital cash, and secret sharing techniques. Prerequisite: MATH 053 with a "C-" or better or permission of instructor.

**MATH 152. Vector Analysis. 4 Units.**

Vector analysis and topics for students of applied mathematics, physics and engineering are studied. Topics include vector fields, gradient, divergance and curl, parametiric surfaces, line integrals, surface integrals, and integral theorems. Formulations of vector analysis in cylindrical and spherical coordinates are also included. Prerequisites: MATH 055 with a "C-" or better.

**MATH 154. Topology. 4 Units.**

This course introduces general topology and its relation to manifold theory. Topics include metric spaces, general spaces, continuous functions, homeomorphisms, the separation axioms, connectedness, compactness, and product spaces. Prerequisite: MATH 049 with a "C-" or better.

**MATH 155. Real Analysis I. 4 Units.**

This course focuses on properties of real numbers, sequences and series of real numbers, limits, continuity and differentiability of real functions. Prerequisites: MATH 049 and MATH 055 with a "C-" or better.

**MATH 156. Real Analysis II. 4 Units.**

This course covers integration, series of real numbers, sequences and series of functions, and other topics in analysis. Prerequisite: MATH 155 with a "C-" or better.

**MATH 157. Applied Differential Equations II. 4 Units.**

This course covers partial differential equations, derivation and solutions of the Wave, Heat and Potential equations in two and three dimensions as well as Fourier series methods, Bessel functions and Legendre polynomials, and Orthogonal functions. Additional topics may include Fourier integral transform methods, the Fast Fourier Transform and Sturm-Liouville theory. Computer exercises that use MATLAB are included. Prerequisite: MATH 057 with a "C-" or better.

**MATH 161. Elementary Concepts of Mathematics I. 4 Units.**

Concepts of arithmetic and geometry underlying elementary school programs in mathematics are studied. Laboratory materials are used to reinforce understanding of concepts. Prerequisite: MATH 003 or higher with a "C-" or better, or appropriate score on the algebra placement test. Not open to freshmen this course does not count as an elective for a BS degree.

**MATH 162. Elementary Concepts of Mathematics II. 4 Units.**

Students study the development of arithmetic and geometric concepts within a classroom setting. The course includes related topics such as diagnostic/prescriptive techniques, the use of calculators and computers, approaches to a K-8 math curriculum and current trends within mathematics education. The course includes field experiences, seminar discussions and laboratory workshops. Prerequisite: MATH 161 with a "C-" or better, or permission of the instructor.

**MATH 164. Topics in History of Mathematics. 3 Units.**

Topics in mathematics are studied from a historical perspective. Topics are chosen from: numeration systems; mathematics of the ancient world, especially Greece; Chinese, Hindu and Arabic mathematics; the development of analytic geometry and calculus; and modern axiomatic mathematics. Students solve problems using historical and modern methods. Students read and report on the biography of a mathematician. Prerequisite: MATH 053 with a "C-" or better. Junior standing or permission of the instructor.

**MATH 166. Mathematical Concepts for Secondary Education. 3 Units.**

This course covers secondary school mathematics from an advanced viewpoint and pedagogical perspective. Content is aligned with the mathematics subject matter requirements from the California Commision on Teacher Credentialing. Prerequisite: MATH 053 with a "C-" or better.

**MATH 168. Modern Geometries. 4 Units.**

Selected topics in this course are from Euclidean, non-Euclidean and transformational geometry in additionto both analytic and synthetic methods. The history of the development of geometries and axiomatic systems is covered. The course uses laboratory materials and computer packages used to reinforce understanding of the concepts. The course is required for high school teacher candidates. Prerequisite: MATH 049 with a "C-" or better or permission of instructor.

**MATH 174. Graph Theory. 4 Units.**

This course is an in-depth consideration of discrete structures and their applications. Topics include connectivity, Eulerian and Hamiltonian paths, circuits, trees, Ramsey theory, digraphs and tournaments, planarity, graph coloring, and matching and covering problems. Applications of graph theory to fields such as computer science, engineering, mathematics, operations research, social sciences, and biology are considered. Prerequisites: MATH 051 or MATH 074 or COMP 047 with a "C-" or better or an appropriate score on the calculus placement test.

**MATH 189A. Statistical Consulting Practicum. 2 Units.**

While working under close faculty supervision, students gain valuable practical experience in applying statistical methods to problems presented by University researchers, business and industry. Students enrolled in MATH 189A ordinarily participate in more sophisticated projects and take a more responsible role than students in MATH 089A. Pass/No credit. Prerequisites: for MATH 089A, MATH 130 with a "C-" or better or permission of the instructor; for MATH 189A, 089A with a "C-" or better and permission of the instructor.

**MATH 191. Independent Study. 2-4 Units.**

Student-initiated projects cover topics not available in regularly scheduled corses. A written proposal that outlines the project and norms for evaluation must be approved by the department chairperson.

**MATH 197. Undergraduate Research. 2-4 Units.**

#### Learning Outcomes

1. Students will demonstrate proficiency in calculus.

2. Students will demonstrate retention of calculus knowledge.

3. Students will demonstrate proficiency in linear algebra.

4. As appropriate to their area of concentration, students will demonstrate proficiency in a breadth of mathematical theory and application.

5. Students will demonstrate the ability to research a topic, summarize, and report findings.

6. Students will be able to function on a team and work collaboratively.

7. Students will be able to convince peers of the validity of a solution.

8. Students will demonstrate proficiency in solving routine mathematical problems.

9. Students will demonstrate proficiency in solving non-routine mathematical problems.

10. Students will demonstrate proficiency in proving mathematical statements.

11. Students will demonstrate proficiency in mathematical modeling.

### Mathematics Faculty

Larry Langley, Associate Professor and Chair, 2001, BS, U.C. Santa Cruz, 1988; AM Dartmouth College, 1990; PhD, Dartmouth College, 1993.

Aleksei I. Beltukov, Associate Professor, 2004, BS, Mendeleyev University, 1994; MS, Mendeleyev University, 1996; MS, Tufts University, 1996; PhD, 2004.

Mouchumi Bhattacharyya, Professor, 2000, BS, Cotton College, 1988; MS, Delhi University, 1990; MPhil, 1992; PhD, University of Wisconsin, Milwaukee, 1999.

Jialing Dai, Associate Professor, 2006, BS, Southwestern Normal University (China), 1985; MS, Jilin University of Technology (China), 1987; MS, University of Arizona, 1998; PhD, 2000.

Alex Dugas, Assistant Professor, 2010, BS, Stanford University, 2000; PhD, University of California, Berkeley, 2006.

Christopher Goff, Professor, 2002, BS, BA, University of Texas, Austin, 1993; MA, University of California, Santa Cruz, 1995; PhD, 1999. Member, Phi Beta Kappa.

John Mayberry, Associate Professor, 2010, BA, California State University, Fullerton, 2003; MA, University of Southern California, 2004; PhD, University of Southern California, 2008.

Sarah Merz, Professor, 1995, BA, Whitman College, 1991; MS University of Colorado at Denver, 1994; PhD, 1995. Member, Phi Beta Kappa

Dennis Parker, Associate Professor, 1985, BSE, University of Oklahoma, 1974; MNS, 1978; PhD, 1985.

Keith E. Whittington, Professor, 1987, BS, University of California, Riverside, 1975; PhD, University of Texas, 1980.