Tom Roby's Math 3240Q Home Page Fall 2023
Applied Linear Algebra

Questions or Comments?

• For questions about thecourse material or structure: Please ask in the appropriate discussion forum in Zulip. (If you ask me such questions by email, I will redirect you there.)
• For questions about using HuskyCT: Once you are logged in to HuskyCT, click Student Help in the top bar.
• For questions about enrollment, your individual circumstances, or suggestions for improving future versions of the course: Please email me: Tom Roby (delete initials from end).
• My Homepage: http://www.math.uconn.edu/~troby
• Office: MONT 239; Phone: 860-486-8385 (but this semester I'll be rarely there).
  
• Office hours: over Zoom, at the link: https://mit.zoom.us/j/95685834389. Feel free also to catch me right after class. I am happy to schedule appointments by email, which I check frequently.

Class Information

COORDINATES: This class is hybrid, but mostly online, synchronous over Zoom. Classes meet Tues/Thurs 11:00–12:15 over Zoom. (The link is in HuskyCT.) Please come to class ready to engage with the material. There is also a Zulip discussion board (see below), which is the best place outside of class to ask questions.

PREREQUISITES: Math 2710 (Transition to Higher Math)

TEXT: We will be loosely following the text Number Theory and Geometry by our own Alvaro Lozano-Robledo, which he has made freely available. We will also use some of the short expository blurbs on number theory written by our own Keith Conrad.

WEB RESOURCES: The homepage for this course will be available and updated at http://www.math.uconn.edu/~troby/math3240f23.

HuskyCT: We will make use the HuskyCT LMS, supplemented with tools that work better. A copy of the course schedule will be posted there that includes links to worksheets, HW exercises, and some solutions (which are for your personal use only, not to be shared). You will turn in worksheets and homework assignments in Gradescope via Husky CT. For classroom discussions, we will use Zulip (see below).

GRADING: Your grade will be based on a single midterm exams, a final exam, worksheets, homework and participation.

EXAMS: The midterm date is already scheduled for 26 October (Thursday), so please mark your calendars now. The final exam is scheduled by the registrar around mid-semester. All exams (like math itself at this level) are cumulative. No makeups will be given; instead if you have an approved reason for missing a midterm, your other exams will count for the appropriately higher percentage. If you miss the final for reasons approved by the Dean of Students and you have completed at least 2/3 of the assignments, then you will have one chance to take a make-up final exam in the second or third week of the following term. I reserve the right to give a followup oral exam to verify your understanding if there are any questions about academic integrity

STUDENT WORKFLOW: For each class you should:

1. Read the recommended sources, or find better ones on the web.
2. Complete the WORKSHEET PROBLEMS and SUBMIT them by the deadline (FRIDAY at NOON).
3. USE the ZULIP DISCUSSION BOARD or CLASS SESSIONS anytime you get seriously stuck;
4. CHECK your WORKSHEET against the SOLUTIONS (posted the morning after the due date);
5. READ the TEXTBOOK to fill in gaps, see an alternate presentation, straighten out confusing points;
6. DO as many HOMEWORK problems as you can. them by 11:59PM WEDNESDAY of the following week.
7. CHECK your HW against the solutions (posted the morning after the due date);

DISCUSSION BOARDS: The Zulip discussion board allows you to ask questions and interact with one another (and the instructor) between class meetings. The quality and quantity of your posts count towards your participation grade. If you don't have questions, please try to help out your fellow students who might be confused, or post asummary of the video lecture.

PARTICIPATION: Class participation, discussion posts, and completing course surveys all count towards your participation grade. This includes keeping your webcam on so that you are visible during online sessions, except for brief periods where you have an important reason for turning it off. (If you have a special situation around this, please check with me privately.)

WORKSHEETS: Every week has a worksheet of basic problems, which you will be working on during classtime and afterwards Worksheets are due by NOON Friday on Gradescope. These will be graded for completion rather than accuracy.

GRADESCOPE: You will turn in your completed worksheets, HW, and even midterm exams using the Gradescope tool that is integrated into HuskyCT. If you click on an assignment there, it will take you to Gradescope. It greatly facilitates my ability to grade exams and give you feedback. Please upload every file as a clear (easily readable) pdf scan, and be careful that you are not casting a shadow over you work if you use your phone to take a picture.

HOMEWORK: Will be assigned for each week, and is due in HuskyCT/Gradescope by 11:59PM WEDNESDAY of the following week.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. Equally importantly, it is a poor learning strategy.

LATE/UNREADABLE ASSIGNMENTS: Late homework and worksheets (up to 48 hours beyond the 2-hour grace period) will receive half credit, after that none. Homework and worksheets that are not easily readable (e.g., because of bad photo quality) will not be graded and will not receive credit. Various smartphone scanning apps can help produce very readable PDF images of your work.

SOFTWARE In trying to understand properties of integers, we will often want to generate some data. Doing some computations by hand is generally good for learning, but having software that can do bigger computations or check your works is very useful. One free source on the web is WolframAlpha. For a full-fledged progamming environment, check out the free open-source computer algebra system called Sage.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used unless otherwise specifically indicated on the exam.

CONTENT: Number Theory is a fascinating subject. It's richness and beauty has captured the imagination of the greatest mathematicians from antiquity to the current day. Once thought to be some of the purest (read "most useless") branch of mathematics, it is now one of the most important: Many of the most important cryptographic systems, including some crucial to everyday web commerce, are based on deep unsolved problems in number theory.

APPLICATIONS: This class may be your only chance to understand the theory of linear algebra, i.e., why things work the way they do. In the future, this deeper understanding will be your key to harnessing the power of this subject to solve the problems that come up in your own work. We need all the time we have to get to the most important tools, e.g., the Singular Value Decomposition (SVD), leaving unfortunately little time to focus on applications. The text has a sections on applications sprinkled throughout, and I encourage you to read them as you have time, during or after the term, particularly ones relevant to your current career path.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible (BUT NO LATER THAN END OF WEEK 2) if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency. In particular, CSD wants a great deal of lead time for scheduling exams.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Take advantage of the online discussions and office hours and the wealth of information on the web.

Web Resources

• The videos and animations available through 3Blue1Brown are highly recommended (not just for linear algebra).
  
• The Prime Pages.
  
• A current list of known Mersenne primes, ordered by the (prime) exponent. Click here to join GIMPS (the Great Internet Mersenne Prime Search).
  
• A discussion of Euclid's algorithm. There are links to other items from number theory at the bottom of the page.
  
• Biographies of Mersenne, Fermat, Euler, Gauss, Dirichlet, and Riemann.
  
• An interview with Jean-Pierre Serre, one of the most prominent number theorists of the 20-th century.
  
• Here's an Online Mind Reader. Can you figure out how it works?

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