Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 189: Advanced Problem Solving
Approved: 2014-02-06, Jesus DeLoera

ATTENTION:

All students must have completed at least 24 units in upper division mathematics courses (above 100). The target audience is advanced juniors or seniors.

Units/Lecture:

3 units

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
See instructor

Prerequisites:

MAT 25, (MAT 22A and 108) or 67

Course Description:

The aim of this course is to have students use all that they have learned within a single quarter-long project that brings together several themes covered in the academic courses in their particular major. This course is unlike any other at our program, as students are exposed to a role played by mathematicians in solving problems (not just homework sets!) and how mathematical thinking is translated into action. The course will lead students to make connections in their course knowledge and to fill gaps when necessary. The students will develop skills for communicating mathematics, both in writing and verbally, in formal and informal environments.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

Week 1


Lectures 1, 2 & 3: Choosing a good capstone project, examples of (realistic) projects and how to choose a project. Guidelines for effective research. Discussion possible areas of exploration suitable for undergraduates (examples of past projects, suggestions cover all areas of mathematics and its applications, 15 different projects discussed).

During first week students meet/discuss with the professor to discuss their interests and decide on a quarter project. Student will form teams (roughly 3 students each) and together explore one of the following seven possible areas (relevant courses are indicated):

  • Mathematics of elections and dividing things fairly.(135AB,145,168,167,133, 160)
  • Mathematical problems arising in Sports and Games.(145,168,167,160,135AB)
  • Mathematical problems Scheduling, planning, and information (148,135AB,145,160,168,133)
  • The art of solving equations (150ABC,115AB,128ABC, 165,119,118)
  • Combinatorics, Geometry and Topology (141,114,145,147,116,146)
  • Mathematics and Art (111,141,125AB, 150ABC,115AB, 129)
  • Other topics? Only with approval of professo!r
      WARNING:Decisions on projects must be finalized no later than lecture 6. Students begin giving oral presentations to all the group on what they will do.

Week 2

Lecture 4: General guidelines for giving technical or scientific oral presentations (e.g, time, design of slides, content organization, how to organize a blackboard presentation). Introduction to LaTEX slides, powerpoint. “Preparing a Poster”. Teaching mathematics and talking to non-mathematicians.

Lecture 5: General guidelines for good writing (Strunk and White). Discussion of Zinsser' book that explores the idea of writing as way of learning. Good writing reflects/helps clear thinking. Guidelines for Mathematical & Scientific writing guidelines.

Lecture 6: Students officially start on their projects today. Presentations will begin, maximum of 5 slides. More on using LaTEX. Using Mathscinet, ZentralBlatt, BibTEX (bibliographic tools).

Week 3


Lecture 7: Students oral presentations in front of class, describing their projects.

Lecture 8: Students oral presentations in front of class describing their projects.

Lecture 9: Students oral presentations in front of class describing their projects.

Week 4


Lecture 10: Selected advanced topics from Mathematical Sciences that may help on projects (see sources). Relation to undergraduate mathematics coursework at UCD and how topics interrelate.

Lecture 11: Selected advanced topics from Mathematical Sciences that may help on projects (see sources). Relation to undergraduate mathematics coursework at UCD and how topics interrelate.

Lecture 12: Selected advanced topics from Mathematical Sciences may helpon projects. Relation to undergraduate mathematics coursework at UCD and how topics interrelate.

IMPORTANT: First written Draft of project due today (end of fourth week). Students exchange papers and will receive comments from each other and from professor.

Week 5 (halfway)


Lecture 13: Problem solving strategies and how to develop a project. What is a proof and methodologies one can use to arrive to one.

Lecture 14: Problem solving strategies and how to develop a project. What is a model and the role of data and computers? Tools of applied Mathematics.

Lecture 15: Problem solving strategies and how to develop a project.

Weeks 6


Lecture 16: Discussion on careers in the mathematical sciences. Networking for jobs.

Lecture 17: Guest lecture from industry, discussion on non-academic jobs.

Lecture 18: Graduate school: is it for you?

IMPORTANT: Second draft version of projects due today.

Weeks 7


Lecture 19: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

Lecture 20: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

Lecture 21: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

IMPORTANT: Third draft version of projects due today.

Weeks 8


Lecture 22: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

Lecture 23: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

Lecture 24: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class.

IMPORTANT: All students hand in fourth draft version of their projects.
Last round of comments prior to final presentations/final version.

Weeks 9,10 & Finals-week.


Final presentations begin continue until finals week (max 25 minutes long per presentation). TA and Professor hear evaluate the presentations using rubric. Students expected to attend some presentations besides their own.

Learning Goals:

As a capstone class this course will put to use and test many of the skills learned in prior courses. For many undergraduates, this is the first chance to write a long-term project (7 weeks to prepare and develop). Students also have oportunities to write rigorous proofs and how to clearly deliver mathematical thinking orally. Students work in teams to solve challenging problems testing and honing their abilities to work in groups.

Assessment:

Project Drafts, Project Report, Oral Presentation, Quizzes