MAT 189 is open to other majors only with permission of instructor. All students must have completed at least 24 units in upper division mathematics courses (above 100). The target audience is seniors (very advanced juniors with permission of instructor).
The aim of this course is to have students use all that they
have learned during their studies within a single quarterlong project
that brings together topics 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
large 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.
The course will be graded with the project, oral presentations, and
various drafts. There will be a few exercises and quizzes along the way.
References: The following resources will be used (the prices of these resources are very affordable). NONE is required for purchase.
First to review all the math you are supposed to know:
On the topic of writing math and solving problems, I will use:
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 longterm project (7 weeks to prepare and develop) and to do real advanced research (REU style). 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.
Prerequisite and Expectations
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 select a project with help from professor. Student will form teams (roughly 3 students each) and together develop the project. Here are some past areas of research (relevant courses are indicated): Check below for current offering.
WARNING: Decisions on projects must be finalized no later than lecture 3. Students will 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. How to prepare a Poster. Teaching mathematics and talking to nonmathematicians. 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 nonacademic 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. 

Weeks 9,10 & Finalsweek. 
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. 
Grading:
The grades will be calculated using the
average and standard deviation of the class. 100 points are possible
which will be divided as follows: