# Mathematics

The Department of Mathematics offers two distinct graduate programs in mathematics. The Master of Science program blends theoretical material necessary for further graduate work in mathematics with basic applications for the student who wishes to enter industry or government work in mathematics. The second program is the Master of Arts Degree for high school teachers. These programs reflect the standards of the National Council of Teachers of Mathematics (NCTM) and the recommendations of the Mathematical Association of America (MAA). The courses combine mathematical topics related to the curriculum with enrichment material which is directly applicable to the classroom.

**Master of Arts**

This is a terminal degree for **high school** teachers of mathematics and this program is accepting applications. Please note that the MA for **middle school** teachers is **not** accepting applications as this time.

__Program Learning Goals__

Students will:

- Develop an in-depth integrated knowledge of topics related to the high school mathematics curriculum.
- Be able to gain advanced competence in communicating mathematical ideas and presenting mathematical arguments both in writing and orally, using proper mathematical notation and terminology.
- Master mathematical concepts that they will be able to use to enrich their high school curriculum.
- Be able to distinguish coherent mathematical arguments from fallacious ones and to construct precise arguments of previously seen or related results with the goal of teaching their students the importance of giving complete explanations of mathematical ideas.
- Be able to synthesize material from multiple perspectives and make connections with other areas of mathematics.
- Be able to use mathematics teaching technology appropriate to each mathematical topic.

Our program is designed for teachers who have a strong desire to increase their knowledge of mathematics in a program designed specifically for them. The emphasis is on exposing teachers to many of the most interesting ideas in mathematics and deepening their understanding of the topics that they themselves teach. Those who earn an M.A. degree in this program will be among the most highly qualified teachers of middle school mathematics in the country.

Here are some reasons for joining our program:

- Continue your professional development by studying mathematics that is relevant to your teaching.
- Become an even better math teacher.
- Interact and share ideas with other math teachers.
- Earn graduate credits or a master’s degree.
- Reinvigorate your interest in the subject of mathematics.
- Enhance your standing in your school district with a graduate degree in mathematics.

**Program for High School Teachers**

Students in the Master of Arts Program in Mathematics for High School Teachers must complete 10 courses, including at least six courses numbered 500‑519. These 500‑level courses are specially designed to utilize the background and meet the needs of high school teachers. None of the graduate courses from the program for middle school teachers are allowed. Courses are offered in a three-year summer cycle, and also in evenings during the fall and spring semesters. A student may complete the required courses by taking courses during two consecutive summers and the intervening school year, or in three consecutive summers.

**Requirements for the Degree**

- Ten courses (30 semester hours) in mathematics, including at least six courses numbered 500‑519.
- An expository essay.
- A comprehensive examination.

**Admission** **Requirements**

- State certification or licensure to teach mathematics in high school.
- A minimum 2.5 GPA in mathematics. If you do not meet these criteria, provisional admission may be granted under certain circumstances.
- A completed application.
- Official transcripts from all institutions attended.

**Courses**

The 12 different summer M.A. courses have been carefully designed to explore mathematical topics that all teachers should be familiar with. They include topics that range from applied mathematics to ideas that display the beauty and excitement of the subject. The following list of courses includes the rationales for program inclusion:

- Mathematical Structures: Patterns and properties that both distinguish and unite ideas of algebra and geometry.
- Discrete Mathematics: High school courses now include the study of matrices, combinatorics, and iterative processes.
- Modern Geometry: You can’t really understand Euclidean geometry unless you have seen non-Euclidean geometry.
- Curves, Surfaces, and Space: Explore the geometric idea of shape and how it relates to the shape of the universe.
- Topics in Calculus: Refresh and deepen your understanding of calculus. It may come in handy.
- Statistical Literacy: An understanding of statistics is playing a larger role in society and in the high school curriculum.
- Great Moments in Mathematics: Relive the journey that brought us to the current state of our art.
- Mathematical Potpourri: Those fascinating ideas you wish you had seen as an undergraduate.
- Technology in the Teaching of Mathematics: Graphing calculators, geometry software, web pages, and more.
- Computer Science for High School Teachers: How do you get a computer to do exactly what you want it to do?
- Problems in Mathematics: Learn problem-solving strategies inspired by the high school American Mathematical Competition (ACM).

**Master of Science**

**THE MS IN MATHEMATICS IS NOT ACCEPTING APPLICATIONS AT THIS TIME.**

__Program Learning Goals__

Students will:

- Develop an in-depth integrated knowledge in Algebra and Analysis as well as multiple elective areas of mathematics, beyond the undergraduate level. They will analyze foundational theorems in much greater depth and exceeding what is expected of an undergraduate mathematics major, and give complete proofs of these advanced theorems.
- Be able to communicate mathematical ideas and present mathematical arguments both in writing and orally, using proper mathematical notation and terminology at an advanced level that represents formal mathematical practice.
- Be able to give complete solutions to challenging graduate-level mathematical problems.
- Be able to synthesize material from multiple perspectives and make connections with other areas of mathematics.

The Master of Science program at John Carroll University combines the classical tradition of pure mathematics with the option of coursework in applied mathematics. Faculty are committed to providing close personal attention to students in a high quality academic environment; at John Carroll, student-faculty contact is the norm rather than the exception. Students frequently use the M.S. program as a stepping-stone for further graduate study. Graduates of our program have a competitive edge when applying to doctoral programs in mathematics. Our M.S. program has been especially attractive to students who want to begin their graduate studies in a small program where their progress is carefully monitored and their success is nurtured. Graduates of our program have established careers in business, industry, government, and education. Their graduate degree has played a major part in their success. Of course, the primary reason students continue their education in mathematics is because of the intellectual excitement it provides. Mathematics is one of the great achievements of the human mind.

All Master of Science students must complete 10 courses, including at least six of the eight courses numbered 531‑579. These courses form the core of the program. None of the graduate courses from the Master of Arts programs are allowed. The material from MT 341, 342, elementary abstract and linear algebra, is presupposed in all Master of Science courses. The material from MT 431, Advanced Calculus of one Variable, is presupposed in all 500-level Master of Science courses.

The courses required for the degree are offered in a two‑year cycle, so that a full-time student may fulfill the requirements for a degree in two years. A part‑time student may complete the requirements in three years. Part‑time students may take at most two courses a semester. A schedule of applicable courses for this degree is available in the Mathematics Department.

**Requirements for the Degree**

- 10 courses (30 semester hours) in mathematics, including at least six courses numbered 531‑579.
- A research paper.
- A comprehensive examination.

**Admission** **Requirements**

- A minimum of seven post-calculus mathematics courses, preferably including abstract algebra, linear algebra and advanced calculus (or real analysis). If you have not taken all of these courses, one or more of them may be taken as part of the program.
- A minimum 2.8 GPA in mathematics. If you do not meet these criteria, provisional admission may be granted under certain circumstances.
- A completed application.
- Official transcripts from all institutions attended.