Writing Exams (And Homework vs. Quizzes)
● Look at past exams
● Avoid “cute” & “interesting” problems
○ maybe one or two (near end)
● Try to get a set performance level in advance (e.g. aim for a median of 70-80)
● Be careful with long or multi-part questions
○ If students mess up the first part, will they be able to get partial credit?
○ In a multi-part question, can give alternative answer for later parts. (If you can’t get part (a) assume its 5 and do the rest of the problem.)
● Check Exam
○ Best to have someone else check it (TA/other instructor)
○ Or wait a day and check it yourself.
● Time the Exam. Students take about 2.5-3x longer (maybe 5x in 10 series)
● Use as a teaching/learning tool
○ If there is something you want students to know for the second half of the class, but it on the midterm.
● Quizzes vs. Homework
○ Homework takes longer to grade (more department resources) but ensure students actually do all the homework.
○ Quizzes work best in large classes (due to grading) but do take up class time.
Other Evaluations
● Presentations
○ One Idea(Eggers does this for 109 sometimes): Assign student to groups of 4-
6(or have them pick groups). Each group is assigned a problem to present.
Pick one person to start presenting then make them switch off midway through.
Offer as Extra Credit so students want to do it.
■ Really when everyone is getting extra credit, no one is.
● In a survey, it was found that public speaking is a major component missing from engineering curriculum.
● Also good to get students to talk among themselves, as a learning tool.
○ Group work on handouts have proven an effective teaching tool.
● In a group, you may want to assign tasks - someone to report to instructor, someone to write down the work, someone to present.
How to Run a Class
● Lecture
○
What is the problem? (e.g )
○ Work through problem motivated new integration technique.
● Use Props or Projector
○ Wolfram Demonstrations!
● Worksheets
● Problems/Discussion (Eggers sometimes does just this for 109)

● Presentation (students present sections) /Seminar
How to Tailor to Different Backgrounds
● (Lower Level) Placement exam/Online system to find where students need help and provide with extra help
● Give students optional problems (perhaps related to their major)
Changing Student Expectations
● Peer or self assessment
● Having exams early enough so that students can drop
○ Students will believe your expectations after the first exam
● Harder First Exam to make students know what are expected from them
Applying for Jobs
From a Search Committee Point of View (Eggers)
● Make sure to include everything asked for
○ e.g. Diversity Statement
○ If missing letters, you may still make first cut
● Think about the people looking through
○ Type set application so easy to follow
○ Make everything easy and pleasant to read
○ Make a good first impression
○ “Send flat” (big envelope) and on nice paper
■ Not really relevant for online submissions
● Math Jobs does most of these things for you
○ Used for almost all research jobs and most teaching jobs
○ some on SIAM(?) site
● Easy to submit one statement for each category and submit to all schools
○ DON’T DO THIS!
● Make a couple of different research/teaching statements
○ some that emphasize teaching/some that emphasize research
○ tailor a bit for each school
● Make cover letter highly specified for each school
○ mention why you want to go there
○ who you want to work with
○ why you would be a good fit
● Length (cover letter and all)
○ Eggers - “a one page kinda guy” maybe 1.5 for each document
○ Patrick Driscoll - Research statement about 4 pages
○ C.V. can be longer - list all publications
Teaching Statement
● Mention:
○ teaching experience
○ goal of teaching
○ what do you think teaching is?

○ What do you do when you walk into a classroom
○ include anecdotal evidence
■ everyone likes a good story
Research Statement
○ Readable for someone not in your filed, general mathematicians
○ What is your thesis about?
○ Mention how to include undergraduates in your research (especially for teaching geared schools)
○ Tailor to people there who you want to work with
■ how does your research relate to their work
● cite their work where appropriate
○ Make most of it accessible to general math audience
■ Some parts that experts in your area can “grab on to”
■ Make analogies to other parts of math
Getting Noticed
● “Cold e-mail” people at schools you are applying that work in the same area as you do, so they recognize your name
● Schools Patrick got interviews at
○ Former student from Advisor
○ Undergraduate Institution
○ Place where he had e-mailed a Faculty member
● Networking - go to meetings
○ Give a talk (esp at JMM)
Putting together your application
● Peer assessment
○ Get someone to proofread etc.
○ Reading other peoples statements will help you find gaps in yours
● Look up interview questions online
○ PRACTICE!
What type of grants are available?
● NSF Grants
○ For graduate students, postdocs, researchers, REUs mostly everyone
● For graduate School
○ NSA
○ DOD
■ Both of the above pay for graduate school, but you have to work for them afterward.
○ NSF
● For Postdocs
○ NSF has a postdoc researcher grant
■ Apply for when you are applying for jobs at the end of grad school
○ There are also early career grants

■ SLOAN
■ Simmons
○ Project Next
■ Early career teaching
■ Networking/forum
● For organizations
○ MAA has grants for groups promoting diversity or women in math
■ AWM has one of these - Tensor grant
The application process
○ Most websites will be list all the materials that you need to submit
○ There is usually a contact person who you can contact with questions
○ OK to use “self-plagiarism” and get ideas for other peoples grants but don’t plagiarize
○ Let the administrators(office staff) know early when you are submitting a grant
○ When are looking for grants to apply to ask other people in you field/position who have recently applied for grants
■ Also, there is usually and group on campus who deals with these things, career services(?)
● BYU has recently started CURM (Center for Undergraduate Research in Mathematics) which brings in professors from other schools to discuss how to set up a research program and then funds them throughout the school year (to have slightly less teaching load(etc) so that they can carry out undergraduate research projects with students throughout the year.
○ Ask Angela Hicks for more information
7 Things Characteristic to a Good Undergraduate Research Problems
From this BYU group
1. Interesting to student, professor and mathematical community(i.e. the results are publishable)
2. Limited amount of background material required to understand the problem.
3. Specific and Concrete nature to the problem
4. Exploration by computation, examples, computer
5. Composed of several layers, partial results likely
6. Mentoring professor does not know exactly how to solve but has a good idea of an approach (that should work)
7. A standard technique exists
Other things that make a good research
● Having a professor/mentor who is dedicated to the project/student
● Providing the student with other undergraduates to discuss research with
● (?) Have graduate students available to answer questions
● A good research problem
○ Where do good problems come from?

■ At Duluth REU, professor send papers, which ask some good questions, also organizer provides additional question when necessary
● Stagger students in research groups (some who will be around next year to help new students who join the group)
● Group project vs. Individual project
○ Different things work for different people
Starting up a Research Program at UCSD (Ideas)
● Pay graduate students over the summer to do research with undergraduates
● Have students work with Advisor/Graduate Student Teams
● Have graduate students apply with a problem in mind
● Have a “long term” research project where you really get to go deep into background and do a project
○ Then even if you don’t prove anything, you’ve still learned something
What worked
● It was good to have students from a variety of backgrounds and levels
● Also had student led/ interest driven discussion
Ideas for next time
● Touch on some more theoretical aspects
○ Perhaps have a different theoretical teaching seminar
○ Discuss things
■ Lockhart’s Lament
■ Alternatives to Calculus
■ Watch videos/ go to classes and discuss teaching methods
● Have observations (observe professors, each other TAing etc)
● Announce the topic in seminar announcements
○ So students can choose to attend specific weeks where the topics interest them
● Have a one day Associate-In Training