# BS in Mathematics

## Overview

The role of mathematics is vital and growing, providing solutions to problems in a wide range of sciences: social, biological, physical, behavioral, and management. As a tool, mathematics is necessary for understanding and expressing ideas in science, engineering and human affairs. Mathematics is integrally related to computer science and statistics, which have proven invaluable to advancing research and modern industrial technology. As a result, employment opportunities in the mathematical sciences are expected to continue to expand.

The Option in Applied Mathematics prepares students either to assume attractive and challenging positions in aerospace or electronics, or to pursue graduate work in pure or applied mathematics.

The Option in Statistics provides a program balanced between theoretical and applied statistics. Students are especially well prepared to pursue a graduate degree. Statisticians find many career opportunities in cutting-edge research in such fields as medicine, pharmaceuticals, business, quality control, and the social sciences.

The Single Subject Credential in Mathematics provides students with the necessary background for obtaining a California Secondary Teaching Credential in mathematics. A fifth year of education courses and student teaching is needed to complete the credential requirements.

### Mission

**SERVICE TO OUR STUDENTS**

The primary mission of the Department of Mathematics and Statistics is to provide high quality mathematics education to a variety of students: to mathematics majors, to students in other majors enrolled in our service courses, to students in our general education courses, and to students in developmental mathematics courses.

**SERVICE TO THE COLLEGE AND UNIVERSITY**

Another mission of the department is to provide a mathematical perspective for our campus colleagues. The department is committed to providing leadership in questions of mathematics and statistics curriculum across the disciplines. We are also committed to providing the technical expertise necessary for campus programs involving mathematical and statistical modeling, simulation, and data analysis.

**SERVICE TO THE COMMUNITY**

In broader terms, we can say that the dissemination of mathematical knowledge is the primary mission of the department, and our audience includes not only university students, but also our colleagues in the regional K-14 mathematical community and their students.

**SERVICE TO THE PROFESSION**

As a community of teacher-scholars, the department has an obligation to contribute to the effort to expand the corpus of knowledge of mathematics and statistics. Mathematical research is inevitably quite technical, highly specialized and, as such, difficult to make accessible to non-specialists. In particular, current research topics seldom filter down to the undergraduate curriculum. What does filter down is the experience, the attitude, and the enthusiasm of those for whom mathematics is a vital, living, and growing thing. Like our students, researchers in mathematics and statistics are engaged in a daily struggle with the subtleties of mathematics.

Research in mathematics education is a different, but equally important, aspect of our mission. We cannot hope to show our students how to solve every mathematical problem they will encounter or even which mathematical method might be effective. We can give our students a toolkit of mathematical approaches to problem solving, and we can give our students some sense of which tools are appropriate for which problems. In broader terms, we can train our students to think mathematically and to reason analytically. Keeping abreast of and contributing to developments in mathematics education will help us help our students and others learn mathematics.

### Goals & Objectives

**General Content:**Graduates are proficient in performing basic operations on fundamental mathematical objects and have a working knowledge of the mathematical ideas and theories behind these operations.**Problem Solving:**Graduates use critical thinking and problem solving skills to analyze and solve mathematical & Statistical problems.**Communication:**Graduates communicate mathematics effectively in a manner appropriate to career goals and the mathematical maturity of the audience.**Proofs Proficiency:**Graduates have a basic proficiency in the comprehension and application of proofs.**Technology:**Graduates know how to use technology tools (e.g., graphing calculators, computer algebra systems) appropriate to the context of the problem.**Life-long Learner:**Graduates are aware of the important role of mathematics and have the interest and ability to be independent learners and practitioners.

### Learning Outcomes

**Goal 1: General Content**

- Demonstrate basic skills and conceptual understanding of differential, integral, and multivariable calculus.
- Demonstrate basic skills and conceptual understanding as relating to fundamental mathematical objects introduced in our degree core, such as, sets, functions, equations, vectors, and matrices.
- Demonstrate basic understanding of probability and statistics, relevant to their option.
- Demonstrate more technical skills and more in depth and broader conceptual understanding in core mathematical areas (such as, analysis, geometry/topology, algebra, applied math, statistics), relevant to their option.

**Goal 2: Problem Solving**

- Interpret and translate problems into appropriate mathematical language.
- Solve problems by applying appropriate strategies and interpreting the results.

**Goal 3: Communication**

- Demonstrate the ability to effectively and accurately write on mathematical topics relevant to their mathematics option and appropriate to their audience.
- Demonstrate the ability to effectively and accurately speak on mathematical topics relevant to their mathematics option and appropriate to their audience.

**Goal 4: Proofs Proficiency**

- Students can read mathematical proofs, extract the key ideas used in the proof, and convey the logic behind the proof.
- Students demonstrate the ability to write their own rigorous and logically correct proofs.

**Goal 5: Technology**

- Students use technology to manipulate mathematical objects (e.g., functions, equations, data sets, etc.)
- Students use technology to conduct mathematical explorations, to model problem scenarios, and to analyze mathematical objects.

**Goal 6: Life-long Learner**

- Students demonstrate the ability to apply mathematics and statistics to new contexts (e.g. in other classes, the workplace, graduate school, classes they teach).
- Students recognize and appreciate the role that mathematics can play in their futures and in society in general.