AS.110.113 - Honors Single Variable Calculus (IBL)

Combined notes for the class.

Nov 28
  • For Mon, Dec 03:
    • HW 12 (final homework!) is due.
    • For the journal, make a table of your Taylor series computations and summarize the chapter.
    • Journal is due. Make sure you've summarized all the integration techniques from the problem sets, this will be very useful to you later.
    • The final project is also due at the end of this week.
Nov 12
  • For Mon, Nov 26:
    • HW 11 is due.
    • There are no reading assignments. Use this time to catch up with your backlog and final project.
    • Have a relaxing Thanksgiving break! Here are some fun videos by Feynman: video 1, video 2, video 3.
Nov 05
Oct 30
  • For Mon, Nov 05:
    • HW 9 is due.
    • Read Chapter 16: π is irrational. Take good notes on whatever you understand, and try to precisely pinpoint out the things you do not.
Oct 24
  • For Mon, Oct 29:
    • HW 8 is due.
    • Read Chapter 16: π is irrational. You can do this in 2 weeks instead of one (I'll post the same reading assignment for the next week). This is a difficult chapter to read, but it is only 4 pages long. The key is to take good notes and be VERY systematic.
Oct 15
  • This Friday (Oct 19) is officially a university holiday. I'll be out of town so won't be able to hold any office hours. Feel free to email me questions, I'll try and respond as quickly as I can.
  • For Mon, Oct 22:
    • HW 7 is due.
    • Journal is due.
    • There's no reading assignment for this weekend.
Oct 10
Oct 03
  • For Mon, Oct 08:
    • Instead of reading new stuff, for this week go back to the problem sets on derivatives and summarize all the theorems. We did a lot in a short span of 2 weeks and it'll be good for you to reflect upon it. Draw lots of pictures and find some good examples in the book/online.
    • HW 5 is due.
    • Added problems for the final project. I would strongly recommend everybody to do some kind of a project.
Sep 25
  • For Mon, Oct 01:
    • Read Chapter 9: Derivatives from the book.
    • HW 4 is due.
Sep 20
  • For Mon, Sep 24:
    • There's no reading assignment for this weekend.
      Instead the journal is due. (I'll return it to you on Wednesday.)
    • We'll be starting with Differentiation next week. So make sure to go over all the chapters we have covered so far and clear out all the lingering doubts.
Sep 16
  • For Mon, Sep 17:
    • Read Chapter 6: Continuous Functions
    • HW 2 is due.
  • For Wed, Sep 19:
    • Read from the beginning of Chapter 8: Least Upper Bounds upto the statement of Theorem 7-1.
  • Information about Final Project updated.
Sep 05
  • Here's a nice paper about the origins of (ε,δ) proofs and the history of Calculus.
Aug 31
  • For Mon Sep, 10:
    • Read the Provisional Definition of Limit from Chapter 5.
    • First HW is due on the same day.
  • For Wed Sep, 12:
    • Read the (ε,δ) Definition of Limit and the adjoining discussion from Chapter 5.
    • Read the Proof of Theorem 1 from Chapter 5.
Aug 30
Aug 25 The website is live. Problem sets etc. will be posted here.

Grading Scheme

40%
Homeworks    

All theory will be developed through problems, essentially you'll learn everything in this class by doing HWs. Each week's problem sets count as one homework, only the best 10 homeworks will be included in the final grade (so no late submissions). Homeworks will be due at the beginning of class on Monday.

20%
Class Participation    

Class attendance is compulsory, if for some reason you are unable to come to class you should let me know beforehand. In class, you'll either be discussing problems in groups or presenting your solutions to others. I'll hand out the relevant problem sets at the beginning of each class. There will be reading assignments which you are expected to read over the weekend.

20%
Journal    

As we will primarily be using HW problems to build all the necessary theory, it will become extremely important to have a good set of notes to refer back to. So, you should take good notes while reading the book! The journal is nothing but a collection of your well-written notes. You'll be asked to submit your journal every few weeks.

20%
Final Project    

See below for details. The final project is due Dec 7.

Final Project

There are two kinds of projects that you can do. You should submit your work at the end of semester (due Dec 7).

  1. If you have never taken Calc 2 before or would like to review whatever you have learnt what feels like a century ago, I'll assign you problems from the Differentiation and Integration chapters when we get to them which you can solve and submit along with the HWs at the end of the semester. This way you don't just learn proofs but also learn/review the computational aspect of Calculus.

  2. You could read a mathematical topic related to Calculus that is typically not covered in a standard Calculus sequence. In this case, you'll have to submit a written report at the end of the semester. The report will have to be written in a Definition-Theorem-Proof format. Some examples include:
    • Topics from Real Analysis (Heine-Borel theorem etc.)
    • Set Theory (construction of reals, axiom of choice etc.)
    • Measure Theory (what is Measure?, construction of non-measurable sets etc.)
    These are just some suggestions, you can come up with your own topics.

Problems for the Final Project (due Dec 7)