# 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.

**Associate Professors:**

- Ramón Figueroa-Centeno, Ph.D.
- Roberto Pelayo, Ph.D.
- Brian Wissman, Ph.D.

**Assistant Professor:**

- Grady Weyenberg, Ph.D.

**Instructors:**

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

The B.A. in Mathematics is offered through two tracks, the Traditional and the Teaching track. Each track requires two years of calculus and one semester each of discrete math and linear algebra. The traditional track includes one-year sequences in the classical areas of modern algebra and real analysis, and students completing this track are particularly well prepared for graduate study. 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 modern algebra. 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 Abstract Algebra and Real Analysis.
- Outcome 3 (Comprehension): Identify, compare, and contrast the fundamental concepts within and across the major areas of mathematics, with particular emphasis on Linear Algebra, Abstract Algebra, 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 Abstract Algebra, Real Analysis, Probability, and Statistics.
- Outcome 3 (Comprehension): Identify, compare, and contrast the fundamental concepts within and across the major areas of mathematics, including Linear Algebra, Abstract Algebra, 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 and CAS, and secondarily spreadsheets, statistical software, and proprietary software such as sketchpad.

## 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.

## Special Aspects of the Mathematics Program

**The Math Center**

College Hall, Room 5
Tel: (808) 932-7531

The Math Center offers free, walk-in tutoring to all students needing help with mathematics (through Calculus I) or with mathematical concepts from other areas. The trained peer tutors have demonstrated a strong understanding of mathematics and a desire to share what they have learned with others.

Students working in the Math Center can use the Center's PCs with access to MINITAB software as well as access the campus wireless network if they prefer to work on their own laptops. The Math Center also provides students access to a quiet study area where they can work independently or in small groups, work on homework, and study for exams.

For more information please visit the Kilohana Math Center website.