# Mathematics

**Department Chair:** Efren Ruiz , Ph.D.

**Email:** ruize@hawaii.edu

**Website:** hilo.hawaii.edu/academics/math/

**Professors:**

- Raina Ivanova , Ph.D.
- Shuguang Li , Ph.D.
- Efren Ruiz , Ph.D.
- Brian Wissman , Ph.D.

**Associate Professor:**

- Ramón Figueroa-Centeno , Ph.D.
- Grady Weyenberg , Ph.D.

**Instructors:**

- Erica Bernstein , Ph.D.
- Zorana Lazarevic , Ph.D.
- Zinat Rahman , M.S.
- Aaron Tresham , M.S.

The Mathematics program is designed to give the undergraduate a broad background in modern mathematics and its applications. The upper-division mathematics courses represent a core leading to further work in mathematics or mathematically related areas or careers in mathematics education. Applications may be pursued in such areas as systems theory, graph theory, number theory, statistics, and geometry, which are widely used in computer science, business, and the physical, life, and social sciences. Students majoring in other fields whose interests require a strong background in mathematics can minor in Mathematics or choose Mathematics as a secondary major.

The B.A. in Mathematics is offered through two tracks, the Traditional and the Teaching track. Each track requires two years of calculus, one semester each of discrete math and linear algebra. The traditional track requires one semester of real analysis and one semester of group theory. The remaining courses for the traditional track can be chosen from upper division mathematics courses and/or select courses from Astronomy, Biology, Computer Science, and/or Physics that fit the students' interest. The teaching track includes a one-year sequence in probability and statistics, consistent with recent National Council of Teachers of Mathematics standards, as well as one semester each in real analysis, geometry, and ring theory. Students completing this broad curriculum are well prepared to teach all areas of intermediate and secondary math.

## Mission

The instructional mission of the Mathematics Department is threefold:

- First, the major program is designed to prepare its students for successful careers in secondary education and other areas requiring a strong foundation in mathematics, or for success at the graduate level, either in mathematics or a related discipline. The degree is intended to familiarize students with a wide range of areas within the field of mathematics, and to instill in them an appreciation for the rigor and structure of the discipline.
- Second, the Math Department provides extensive support to those departments requiring mathematics content for their majors, particularly those in the Natural Sciences.
- Third, the Department services non-science majors by offering a limited selection of courses that are designed to introduce the students to the fundamental concepts that constitute classical and contemporary mathematics.

## Program Goals

**Graduating majors in the Traditional Track should be able to:**

- Outcome 1 (Knowledge): Demonstrate mastery of the core material found in single and multi-variable Calculus and Linear Algebra.
- Outcome 2 (Knowledge): Demonstrate mastery of the core concepts in Group Theory and Real Analysis.
- Outcome 3 (Comprehension): Correctly identify fundamental concepts within and across the major areas of mathematics, with particular emphasis on Linear Algebra, Group Theory, and Real Analysis.
- Outcome 4 (Reasoning): Use a variety of theorem-proving techniques to prove mathematical results.
- Outcome 5 (Communication): Demonstrate the abilities to read and articulate mathematics verbally and in writing.

**Graduating majors in the Teaching Track should be able to:**

- Outcome 1 (Knowledge): Demonstrate mastery of the core material found in single and multi-variable Calculus and Linear Algebra.
- Outcome 2 (Knowledge): Demonstrate mastery of the core concepts in Ring Theory, Real Analysis, Probability, and Statistics.
- Outcome 3 (Comprehension): Correctly identify fundamental concepts within and across the major areas of mathematics, including Linear Algebra, Ring Theory, Real Analysis, Geometry, Probability, and Statistics.
- Outcome 4 (Reasoning): Use a variety of theorem-proving techniques to prove mathematical results.
- Outcome 5 (Communication): Demonstrate the abilities to read and articulate mathematics verbally and in writing.
- Outcome 6 (Application): Demonstrate a level of mathematical sophistication consistent with the ability to develop and deliver all pre-college mathematics.
- Outcome 7 (Technology): Demonstrate an ability to appropriately use technology in the problem-solving process, including graphing calculators, Computer Algebra Systems, and Statistical Software.

## Goals for Student Learning in the Major

As a result of having majored in mathematics, students are expected to develop:

- A general understanding of the different areas of mathematics and how they interrelate, and the importance of mathematics in a scientifically-oriented society;
- Classical theorem-proving skills, which include the ability to reason mathematically and to apply the rigor necessary to construct proofs;
- A refined understanding of the problem-solving process;
- The ability to independently develop and deliver all pre-college math curriculum, if the professional goal is teaching;
- A working knowledge of technology appropriate to the field;
- The skills necessary to:
- Read, write, translate, and articulate mathematically-related material,
- Solve problems using a variety of techniques, including algebraic, numerical, and spatial reasoning through visualization (e.g. graphically),
- Make inferences and generalizations.

## Contributions to the General Education Program

All lower-division mathematics courses **(except MATH 103 Intro to College Algebra (3) , MATH 199 Directed Studies (To Be Arranged) , and MATH 299 Directed Studies (To Be Arranged) )** satisfy the CAS General Education “quantitative and logical reasoning” requirements. Students who have fulfilled this General Education requirement should have developed an appreciation for the applicability of mathematical concepts and techniques to contemporary society.