Basic Information
Schedule: June 6th-July 28th (except the week of July 4th-8th)
Workshop schedule in calendar form: SWILA CalendarHere's what I covered each day of the workshop: SWILA Schedule of Topics
Rooms: 145 Altgeld Hall and 159 Altgeld Hall
Times: 5:00 PM - 6:30 PM on Mondays and Thursdays (switched from 5:30 PM - 7:00 PM)
The first day will run from 5:30 PM - 7:30 PM. We will begin this day by looking at the workshop's syllabus.
Dinner together after class each Thursday (non-participants are also welcome to attend!)
On Mondays, starting June 13, there will be an optional teaching philosophy session after class from 7:00 PM - 7:15 PM.
Email: djjung2@illinois.edu
Office hour: One hour per week, Tuesday or Wednesday, 5-6pm to start? (Ended up not having this)
Cost: Free! :)
Here's the latest draft of my lecture notes: Complete SWILA Notes
Here's all of the problem sets combined into one document: All PSets
Here's the final reflection assignment for SWILA (due the last week of class): Reflection Assignment
I wrote about the process of organizing and running SWILA, why I ran it as I did, about the evaluations written by participants, and the possible future of the workshop: Behind the Scenes of SWILA '16
All the documents associated with SWILA (with LaTex files) are stored in this folder: SWILA Google Drive folder
I didn't upload Tex files for the individual days' notes, but I uploaded the Tex file for the entire set of notes.
Class Notes and Problem Sets
Topics to cover: 1. Vector spaces: C'mon, it's just algebra (except not quite); 1.1. Fields; 1.2. Vector spaces; 1.3. Linear independence; 1.4. Bases and coordinates; 2. Linear transformations: More than meets the I; 2.1. Linear transformations; 2.2. Linear transformations T:F^m to F^l as matrices.
5:30-5:45: Introductions and syllabus; 5 minute break, 5:50-6:40: Lecture; 5 minute break; 6:45-7:30: Problem session; 23 attendees
Thursday, June 9th: June 9th Notes June 9th PSet
Topics to cover: 2.3. The matrix representation of a linear transformation; 2.4 Change of coordinate matrices; 2.5. The trace of a matrix; 2.6. Dimension and isomorphism.
18 lecture attendees; 21 dinner attendees (Joe's Brewery)
Monday, June 13th: June 13th Notes June 13th PSet
Topics to cover: 2.7. Row reduction and the general linear group; 3. Vector spaces: But wait, there's more!; 3.1. Subspaces; 3.2. Direct sums; 3.3. Linear maps and subspaces.
23 students
Went over the teaching philosophy question: In Calc 1 and 2, your students will often be taking their first college math class. What is the typical Calc 1/2 student's perspective on math? (It may be helpful to discuss what "typical" means.)
Thursday, June 16th: June 16th Notes June 16th PSet
Topics to cover: 3.4. Quotient spaces;
4. A minor determinant of your success;
4.1. Determinant of a matrix;
4.2. Computing the determinant of small matrices;
4.3. Geometric interpretation and the special linear group; 5. Eigenstuff: of maximum importance; 5.1. Facts about polynomials.
15 lecture attendees, 18 dinner attendees
Monday, June 20th: June 20th Notes June 20th PSet
Topics to cover: 5.2. Eigenvalues; 5.3. The minimal polynomial; 5.4. Diagonalizability.
13 students
Teaching philosophy question:Imagine that you are a TA of a 30 student 50-minute discussion. Students typically work on worksheets together in groups of 4, but their performance on worksheets doesn't directly impact their overall grades. In one group, 3 of the students work really together, but the fourth student is very behind in the class. So behind, that he cannot really contribute to the group. What do you do? (Remember that your academics should come first.)
Thursday, June 23rd: June 23rd Notes June 23rd PSet
Topic to cover: 5.5. Cyclic subspaces.
15 lecture attendees, 18 dinner attendees
Monday, June 27th: June 27th Notes June 27th PSet
Topic to cover: 5.6 Rational canonical form.
12 attendees
Teaching philosophy question: What percent impact do you have on your typical student's performance in the course? (Again, what does "typical" mean?) For example, 100% means you alone are in complete control of their success in the course and 0% means you have absolutely no effect on their eventual performance.
Thursday, June 30th: June 30th Notes June 30th PSet
Topics to cover: 5.7 The Jordan canonical form; 5.8 Computing the Jordan canonical form.
10 lecture attendees, 18 dinner attendees
July 4-8: No class. I'm going to a conference at Texas A&M. Dinner plans are up to you all.
Monday, July 11th: July 11th Notes July 11th PSet
Topics to cover: 6. Inner product spaces? ... More like winner product spaces!; 6.1. Inner products; 6.2. Angles and orthogonality in inner product spaces; 6.3. Orthonormal bases for finite-dimensional inner product spaces.Teaching philosophy question: Imagine you are a TA of a 30 student discussion, and attendance doesn't count towards your students' final grades. Suppose it's the midpoint of the semester and less than 10 students attend your discussion on non-quiz days. How should you feel about this? What should you do? (Remember that your studies should first.)
11 students
Thursday, July 14th: July 14th Notes July 14th PSet
Topics to cover: 6.4 Orthogonal complements and projections; 6.5 The adjoint of a linear transformation.
Dinner at 6:30 PM, Joe's Brewery
9 lecture attendees, 16 dinner attendees
Monday, July 18th: July 18th Notes July 18th PSet
Topics to cover: 7. Linear operators on IPS: The love story of a couple linear transformations who respected their own personal (inner product) space; 7.1. Self-adjoint maps; 7.2. Isometries; 7.3. The orthogonal and unitary groups.
Teaching philosophy session: It's the end of the semester and energy is wavering in your discussions. What are effective ways (math or non-math) to motivate your students to work hard in the course? (Remember that your energy is also wavering and your studies come first.)
13 attendees
Thursday, July 21st: July 21st Notes July 21st PSet
Topics to cover: 7.4. The spectral theorem for self-adjoint operators.
Dinner at Mia Za's, 6:30 PM
9 lecture attendees, 12 dinner attendees
Monday, July 25th: July 25th Notes July 25th PSet
Topics to cover: 7.5. Normal operators and the spectral theorem for normal operators; 7.6. Schur's theorem; 7.7. Singular value decomposition.
Teaching philosophy question: You just finished your first semester as a merit or Calc 1 TA. You spent an average of 10 hours per week preparing for discussions, you offered an extra 2 office hours per week, made study guides for all the exams, and emailed them once a week giving them an outline of the schedule and important things to study. You expected to earn perfect scores on your evaluations, but instead you rated in the bottom half. Also, one of your friends who spent no time preparing for discussions and was sometimes late scored in the top 10%. How should you feel about this? How should you act upon this?
11 attendees
Thursday, July 28th: July 28 Notes July 28 PSet
Topics to cover: 8. A bird? A plane?... No, it's a chapter about multilinear algebra; 8.1. Dual spaces; 8.2. Tensor products.
Workshop final picture, pass out certificates, closing remarks
Dinner at Thai Place, 6:30 PM
15 lecture attendees, 15 dinner attendees
Daily Agenda
Each class will begin with 40-45 minutes of lecturing by the instructor in 145 Altgeld Hall. During this time, participants may choose to instead work on the day's problem set in 159 Altgeld Hall. After a 5 minute break, participants will work in small groups on a problem set while enjoying refreshments for 40-45 minutes. Each Thursday, everyone will have dinner together after class. On Mondays, participants can stay after for 15 minutes to discuss a teaching philosophy question in small groups.
Prerequisites
Participants should have been exposed to some linear algebra and proof techniques in prior math courses. It is expected that participants are enthusiastic and willing to work with others. All undergraduate and graduate students are welcome to participate.
Monday Teaching Philosophy Sessions
I would like to hold optional teaching philosophy sessions on Mondays after class from 7:00 PM to 7:15 PM. This is intended to be "more" optional than the problem sessions and is intended for participants who are more teaching-focused. I believe that an important common trait among good teachers is the desire to better reach your students and push them to succeed. Thus, a necessary condition is being willing to discuss how to conduct yourself in the classroom and how to better facilitate student collaboration. At the beginning of each session, I will propose one teaching philosophy question which participants will discuss in small groups (3 or 4) for 10 minutes. In each group will be a more experienced TA to help facilitate the discussion. In the last 5 minutes, each group will present their findings. These questions are intended to be open-ended and thought-provoking, and they may draw differing opinions. Some examples are:
1. What are the best things to do the first day of discussion? To achieve?2. In Calc 1 and 2, your students will often be taking their first college math class. What is the typical Calc 1/2 student's perspective on math? (It may be helpful to discuss what "typical" means.)3. Imagine that you are a TA of a 30 student 50-minute discussion. Students typically work on worksheets together in groups of 4, but their performance on worksheets don't directly impact their overall grades. In one group, 3 of the students work really together, but the fourth student is very behind in the class. So behind, that he cannot really contribute to the group. What do you do?4. What percent impact do you have on your typical student's performance? (Again, what does "typical" mean?) For example, 100% means you alone are in complete control of their success and 0% means you have absolutely no effect on their eventual performance.5. Should you hold extra office hours? If so, at what times in the semester should you?6. How frequently should you email students? What do you include in an email? How long should an email be? How long on average do you think your typical student spends reading one of your emails? Anything else about emails?7. Should you provide answers to worksheets? To quizzes?8. What should the general structure of a 50-minute Calc 1 discussion be? (This is typically their first college math class and you have free rein on how to lead discussion.) For example, should you spend more time doing examples on the board or having them work in groups?9. You are a merit or Calc 1 TA. You spent an average of 15 hours per week preparing for discussions, you offered an extra 2 office hours per week, made study guides for all the exams, and emailed them once a week giving them an outline of the schedule and important things to study. You expected to earn perfect scores on your evaluations, but instead you rated in the bottom half. Also, one of your friends who spent no time preparing for discussions and was sometimes late scored in the top 10%. How should you react to this?10. It's the end of the semester and energy is wavering in your discussions. What are effective ways (math or non-math) to motivate your students to work hard in the course? (Remember that your energy is also wavering and your studies come first.)11. Imagine you are a TA of a 30 student discussion, and attendance doesn't count towards your students' final grades. Suppose it's the midpoint of the semester and less than 10 students attend your discussion on non-quiz days. How should you feel about this? What should you do? (Remember that your studies should first.)
Frequently Asked Questions
1. I am a current graduate student and I would like to participate in the workshop! What should I do?
Please fill out the sign up form at the following link: https://www.surveymonkey.com/r/WFKXHH9
2. What if the workshop isn't challenging enough for me?The problem sets will be drawn from a variety of books of varying difficulty. Thus, the exercises should range from following from the definitions to graduate level. Everyone should be able to find problems that are challenging, yet manageable.3. What if the workshop is too challenging for me?See previous answer.4. What if the lectures don't interest me or are taught at too low of a level for me?0. Problem sets will be distributed at the beginning of each class. Students may work quietly by themselves during lectures. Also see previous answer.5. College cost me an arm and a leg. Will this workshop cost me another arm and a leg, thus leaving me without any legs or arms?This workshop is free. You also will not be paid for participating in the workshop.6. I am more of a visual learner and can't really learn much from lectures. Is there any way I could study the lectures by myself and then just come to the problem-solving half of classes?Yes. I should post lecture notes at least a couple hours before each lecture, so you can study by yourself if it better suits you.7. Will the dinners on Thursdays be paid for?Unfortunately, you will have to pay for them yourself.8. How do I know where dinner will be? Are they mandatory?Students should be notified by email at least a day before, and I will post said deets on Facebook. Dinners are not mandatory, but I think attending would be an excellent opportunity to get to know incoming and current graduate students in a laid-back setting.9. Will solutions to problem sets be posted?I will not post solutions. That's all I can say.10. How much time should I expect to spend on this outside of class time?I do not expect that you spend anytime outside of the 3 hours in class per week. You are, of course, free to spend extra time however. I do not want to add extra stress to your life with this workshop.11. What's the point of the problem-solving sessions?I believe that solving exercises is the quickest way to learn linear algebra. Also, I expect that participants will get to know each other better through this and improve their abilities to work with others.12. Do I need to attend every class or can I choose to come to only certain classes?You are not required to come to every class in order to participate in the workshop. Something may come up or you may think that you already know a topic very well. However, I think the workshop will run smoother if more people attend on a regular linearly independent and spanning set of vectors.13. Will grades be assigned? Will my performance in the workshop affect my funding?Grades will not be assigned. Problem sets will be neither turned in nor graded. Participation, attendance, and performance in the workshop will have no effect on your funding.14. I am a current graduate student and I would like to help you organize the workshop! What can I do?Please email me and I will get back to you.15. Can you guarantee that this workshop will be fun?I'd rather promise than imply that SWILA will be fly, but I'd hate be the guy who lies then says bye while you sigh and cry with 1-ply. Though... I'm quite certain that SWILA will be killa', with a side of vanilla.16. Who should I contact if I have any more questions?You should email me at djjung2@illinois.edu
Much thanks to Alyssa Loving and Ruth Luo for helping edit this website!
No comments:
Post a Comment