The Mathematics major prepares you to analyze complex discipline-based issues, synthesize information from multiple sources and perspectives, communicate skillfully in oral and written forms, and use appropriate technologies. The flexibility of the major gives you enough freedom to mold your degree along your particular interest toward a career or graduate school. Many mathematics majors pursue careers in industry (e.g. engineering, finance, business), teaching, and government service immediately upon graduation. Others continue on to graduate school, then pursue careers in research and university teaching.

## Required Courses

### Special Requirements

If you transferred into CSUMB as an AS-T-certified student in mathematics, please see the AS-T certified requirements.

If you are unsure about your transfer status, please talk to a mathematics faculty advisor as soon as possible.

All other mathematics majors, see below.

### Standard Requirements

In order to graduate, you will also need to complete your general education and university requirements.

Complete ALL of the following courses:

- MATH 150: Calculus I
- MATH 151: Calculus II
- MATH 170: Discrete Mathematics
- MATH 250: Multivariate Calculus
- MATH 265: Differential Equations and Linear Algebra
- CST 231: Problm-Solving/Programng
- MATH 300: Major Proseminar
- MATH 320: Applied Probability and Statistics
- MATH 322: Foundations of Modern Math
- MATH 330: Advanced Linear Algebra
- MATH 400: Capstone Seminar
- MATH 410: Modern Algebra I
- MATH 420: Mathematical Analysis I

Complete the general requirements for a Mathematics B.S. or select a concentration from the options below.

### Mathematics (no concentration)

Complete the following courses:

- MATH 411: Modern Algebra II
**OR**MATH 421: Mathematical Analysis II - MATH 361S: Mathematics Tutors
**OR**MATH 362S: Service Learning for Mathematics Consultants

Complete THREE of the following MATH or STAT Electives not counted above:

- MATH 325: Number Theory
- MATH 326: History of Mathematics
- MATH 329: College Geometry
- MATH 340: Ordinary Differential Equations
- MATH 350: Complex Analysis
- MATH 370: Logic and Computation
- MATH 372: Mathematics of Music
- MATH 374: Mathematical Modeling
- MATH 375: Numerical Analysis for Mathematics and Statistics
- MATH 376: Partial Differential Equations
- MATH 385: Enumerative Combinatorics
- MATH 386: Graph Theory and Its Applications
- MATH 395: Special Topics
- MATH 411: Modern Algebra II
- MATH 421: Mathematical Analysis II
- STAT 320: Nonparametric Statistics
- STAT 395: Special Topics
- STAT 410: Applied Statistics Methods: Linear Models
- STAT 420: Statistical Theory I
- STAT 421: Statistical Theory II

### Pure Mathematics Concentration

Complete ALL of the following courses:

- MATH 350: Complex Analysis
- MATH 411: Modern Algebra II
- MATH 421: Mathematical Analysis II
- MATH 361S: Mathematics Tutors
**OR**MATH 362S: Service Learning for Mathematics Consultants

Complete ONE of the following courses:

- MATH 340: Ordinary Differential Equations
- MATH 370: Logic and Computation
- MATH 374: Mathematical Modeling
- MATH 375: Numerical Analysis for Mathematics and Statistics
- MATH 376: Partial Differential Equations
- MATH 385: Enumerative Combinatorics
- MATH 386: Graph Theory and Its Applications
- STAT 320: Nonparametric Statistics
- STAT 420: Statistical Theory I
- STAT 421: Statistical Theory II

### Mathematics Subject Matter Preparation Program Concentration

Complete ALL of the following courses:

- MATH 325: Number Theory
- MATH 326: History of Mathematics
- MATH 329: College Geometry
- MATH 361S: Mathematics Tutors

Complete ONE of the following MATH/STAT Electives not counted previously:

- MATH 340: Ordinary Differential Equations
- MATH 350: Complex Analysis
- MATH 370: Logic and Computation
- MATH 372: Mathematics of Music
- MATH 374: Mathematical Modeling
- MATH 375: Numerical Analysis for Mathematics and Statistics
- MATH 376: Partial Differential Equations
- MATH 385: Enumerative Combinatorics
- MATH 386: Graph Theory and Its Applications
- MATH 395: Special Topics
- MATH 411: Modern Algebra II
- MATH 421: Mathematical Analysis II
- STAT 320: Nonparametric Statistics
- STAT 395: Special Topics
- STAT 410: Applied Statistics Methods: Linear Models
- STAT 420: Statistical Theory I
- STAT 421: Statistical Theory II

### statistics concentration

Complete ALL of the following courses:

- MATH 362S: Service Learning for Mathematics Consultants
- STAT 410: Applied Statistics Methods: Linear Models
- STAT 420: Statistical Theory I
- STAT 421: Statistical Theory II

Complete ONE of the following MATH/STAT Electives not counted previously:

- MATH 325: Number Theory
- MATH 326: History of Mathematics
- MATH 329: College Geometry
- MATH 340: Ordinary Differential Equations
- MATH 350: Complex Analysis
- MATH 370: Logic and Computation
- MATH 372: Mathematics of Music
- MATH 374: Mathematical Modeling
- MATH 375: Numerical Analysis for Mathematics and Statistics
- MATH 376: Partial Differential Equations
- MATH 385: Enumerative Combinatorics
- MATH 386: Graph Theory and Its Applications
- MATH 395: Special Topics
- MATH 411: Modern Algebra II
- MATH 421: Mathematical Analysis II
- STAT 320: Nonparametric Statistics
- STAT 395: Special Topics
- STAT 410: Applied Statistics Methods: Linear Models
- STAT 420: Statistical Theory I
- STAT 421: Statistical Theory II

## Learning Outcomes

### MLO 1 Mathematical Content

**Calculus and Differential Equations**. Students explain and apply the basic concepts of single and multivariate calculus including the various forms of derivatives and integrals, differential equations, their interconnections and their uses in analyzing and solving real-world problems.**Discrete Mathematics.**Students perform operations on sets and use basic mathematical logic. Students represent and solve both theoretical and applied problems using such techniques as graph theory, matrices, sequences, linear programming, difference equations and combinatorics.**Computer Programming.**Students design, develop and document computer programs to solve problems.**Foundations of Modern Mathematics**. Students explain the nature and purpose of axiomatic systems, utilize various methods of mathematical proof and prove fundamental theorems utilizing various axiomatic systems.**Statistics and Probability**. Students use a variety of methods and techniques to determine the probability of an event or events, including the use of density functions and associated probabilities of both discrete and continuous probability distributions. Students work with applications of probability to mathematical statistics such as point estimation and hypothesis testing.**Linear Algebra**. Students set up and solve systems of linear equations using various methods. Students work with vector spaces and linear transformations. Students apply matrix techniques to applied problems from various disciplines.**Abstract Algebra.**Students use a variety of algebraic representations to model problem situations. Students explain the theory of and operations with groups, rings and fields. Students work with advanced algebraic structures and explain how these manifest themselves within the algebra studied in introductory and pre-college mathematics courses.**Real and Complex Analysis.**Students explain the underlying set, operations and fundamental axioms that yield the structure of the real and complex number system. Students apply analytic techniques to real-world problems. Students give a rigorous mathematical explanation of the development of calculus from first axioms.**Area of Concentration Competency.**Students demonstrate depth in a chosen area of mathematics by completing an appropriate sequence of learning experiences.

### MLO 2 Service to the Community

Students demonstrate the ability to combine disciplinary knowledge and community experiences to share the relevance and importance of mathematics with culturally, linguistically, technologically and economically diverse populations in the context of issues of social responsibility, justice, diversity and compassion.

### MLO 3 Problem Solving

Students demonstrate the ability to: (a) place mathematical problems in context and explore their relationship with other problems; (b) solve problems using multiple methods and analyze and evaluate the efficiency of the different methods; (c) generalize solutions where appropriate and justify conclusions; and (d) use appropriate technologies to conduct investigations, make conjectures and solve problems.

### MLO 4 Mathematics as Communication

Students demonstrate the ability to: (a) articulate mathematical ideas verbally and in writing, using appropriate terminology; (b) present mathematical explanations suitable to a variety of audiences with differing levels of mathematical knowledge; (c) analyze and evaluate the mathematical thinking and strategies of others; (d) use clarifying and extending questions to learn and communicate mathematical ideas; and (e) use models, charts, graphs, tables, figures, equations and appropriate technologies to present mathematical ideas and concepts.

### MLO 5 Mathematical Reasoning

Students demonstrate the ability to: (a) reason both deductively and inductively; (b) formulate and test conjectures, construct counter-examples, make valid arguments and judge the validity of mathematical arguments; and (c) present informal and formal proofs in oral and written formats.

### MLO 6 Mathematical Connections

Students demonstrate the ability to: (a) investigate ways mathematical topics are interrelated; (b) apply mathematical thinking and modeling to solve problems that arise in other disciplines; (c) illustrate, when possible, abstract mathematical concepts using applications; (d) recognize how a given mathematical model can represent a variety of situations; (e) create a variety of models to represent a single situation; and (f) understand the interconnectedness of topics in mathematics from a historical perspective.

### MLO 7 Technology

Students demonstrate the ability to: (a) analyze, compare and evaluate the appropriateness of technological tools and their uses in mathematics; (b) use technological tools such as computers, calculators, graphing utilities, video and other interactive programs to learn concepts, explore new theories, conduct investigations, make conjectures and solve problems; and (c) model problem situations and solutions, and develop algorithms (including computer programming).

## Course Pathways

These pathways are examples of how you might complete all the requirements for your degree in an order that makes sense given prerequisites. They are meant to give you a general sense of what your education will look like.

Your own unique situation and a number of other factors may mean your actual pathway is different. Perhaps you'll need an extra math or language class, or one of the courses we've listed isn't offered in a particular semester. Don't worry - there is flexibility built into the curriculum. You'll want to work closely with an advisor and use the academic advisement report to take all that into account and develop a pathway that's customized for you.

In the meantime, use this example as a starting point for choosing classes or discussing your plans with an advisor. Your advisor is your best resource when it comes to figuring out how to fit all the courses you need, in the right sequence, into your personal academic plan.

### Mathematics Freshman Pathway

#### Fall Freshman

* This FYS class is just an example. The FYS class you choose might meet a different GE area, so you would have to adjust your actual pathway accordingly.

#### Spring Freshman

**Course:**Language 201

**Units:**4

**Requirement:**Language Proficiency

#### Fall Sophomore

#### Spring Sophomore

*This is one possible choice for a lower divsion service learning course. If you choose another course be sure that the D1 requirement is still met by the course or another GE course.

#### Fall Junior

**Course:**Concentration Course

**Units:**4

**Requirement:**Concentration

#### Spring Junior

**Units:**5

**Requirement:**Concentration

**Course:**Concentration Course

**Units:**4

**Requirement:**Concentration

#### Fall Senior

**Course:**Concentration Course

**Units:**4

**Requirement:**Concentration

#### Spring Senior

**Course:**Concentration Course

**Units:**4

**Requirement:**Concentration

### Mathematics Transfer Pathway

#### Fall Junior

**Course:**Any approved course

**Units:**4

**Requirement:**

**Units:**5

**Requirement:**Concentration

**Course:**Free Elective

**Units:**3

**Requirement:**

#### Spring Junior

**Course:**Concentration Course

**Units:**4

**Requirement:**Concentration

#### Fall Senior

**Course:**Free Elective

**Units:**4

**Requirement:**

#### Spring Senior

**Course:**Any approved course

**Units:**4

**Requirement:**Concentration

### Subject Matter Preparation Program Concentration Freshman Pathway

#### Fall Freshman

* This FYS class is just an example. The FYS class you choose might meet a different GE area, so you would have to adjust your actual pathway accordingly.

#### Spring Freshman

**Course:**Language 201

**Units:**4

**Requirement:**Language Proficiency

#### Fall Sophomore

#### Spring Sophomore

*This is one possible choice for a lower divsion service learning course. If you choose another course be sure that the D1 requirement is still met by the course or another GE course.

#### Fall Junior

**Units:**4

**Requirement:**Concentration

#### Spring Junior

**Units:**4

**Requirement:**Concentration

**Course:**MATH/STAT Elective

**Units:**4

**Requirement:**Concentration

#### Fall Senior

**Units:**4

**Requirement:**Concentration

**Course:**Open Elective

**Units:**1

**Requirement:**

#### Spring Senior

### Subject Matter Preparation Program Concentration Transfer Pathway

#### Fall Junior

**Course:**MATH/STAT Elective

**Units:**4

**Requirement:**Concentration

**Course:**Free Elective

**Units:**4

**Requirement:**

#### Spring Junior

**Units:**4

**Requirement:**Concentration

**Course:**Free Elective

**Units:**4

**Requirement:**

#### Fall Senior

**Units:**4

**Requirement:**Concentration

#### Spring Senior

**Units:**4

**Requirement:**Concentration