AS.110.113 - Honors Single Variable Calculus

Class : MW 1:30-2:45pm, Hodson 315
: F 1:30-2:20pm, Maryland 217
My office : Kreiger 200
Office Hours : Th 2:00-4:00pm
Help Room : M 11:00am-1:00pm
Email : anakade1 at jhu ddott edu
Textbook : Calculus, 3rd Edition, Spivak

Course updates

Week 1
Proofs
PSet01

Proof techniques

'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean, neither more nor less.'

- Through the Looking Glass

In the first week you'll learn how to write proofs. The notes are from this link. The reading material and the HWs will be handed out in class. This HW is extremely important as throughout the course you'll be doing a lot of proof writing.

Week 2
Ch 5
PSet02

Limits

  • Ch.5: Pages 90, 91, specifically read the example x.sin(1/x).
  • Ch.5: The discussion directly preceding the definition of limit on page 96.
  • Ch.5: Proof of Theorem 2 part (1).
  • Ch.5: Definitions of one sided limits, and limit as x → ∞ on page 104 and 105.
Week 3
Ch 6, 7, 8
PSet03

Continuity & Three hard theorems

  • Ch.6: Definition of continuity of f(x) at a.
  • Ch.6: Proofs of Theorem 1 and Theorem 2.
  • Ch.6: Discussion directly following Theorem 2 about continuity on intervals.
  • Ch.7: From Theorem 1 to the proof of Theorem 9, from page 120 to 124.
  • Ch.8: From the beginning till property (P13) on Pg. 133.
Homework 3 is due on Friday, Sept 22.
Week 4
Ch 9

Differentiation

Reading assigment for Monday:

  • There is no reading assignment for Monday.
    Make sure to go over Limits and Continuity chapters.

Reading assigment for Wednesday:

  • Pg. 147 - 152, the definition of derivative and it's connection to tangents.

Reading assigment for Friday:

  • Pg. 152 - 161, left-hand and right-hand derivative, Theorem 1, higher order derivatives.
  • Homework 3 is due today.
Week 4
Ch 10

Derivatives

Week 6 Ch. 9, 10, 11 Derivatives etc.
Week 7 Ch. 13, 14 Integrals, Fundamental Theorem of Calculus
Week 8 Ch. 12, 15, 18, 19 Integration in practice
Week 9 Integration continued
Week 10 Integration continued
Week 11 Ch. 21 Approximations to Polynomial Functions
Week 12 Ch. 22, 23 Infinite Sequences and Series
Week 13 Ch. 24 Uniform Convergence and Power Series


Course Description

The official syllabus can be found here. This course covers the topics typically covered in the standard Calc 1 and Calc 2 courses, and you will also learn to write mathematical proofs, as such this is a VERY fast paced course. If you like being challenged and are curious and excited about maths this is the course for you. You should not be taking this course simply to meet your course requirements or because of the "honors" in the title of the course. This course will be taught in the mode of Inquiry Based Learning.

Inquiry Based Learning

“The only way to learn mathematics is to do mathematics.”

- Paul Halmos

In this (IBL) course there will hardly be any lectures to prove things for you. Instead, you will prove the propositions yourself and explain your proofs to each other. The IBL format fosters creativity and a deep understanding of the material. However, its success depends heavily on the students: you must be actively engaged and prepared for class every day. On one hand this mode of learning is highly rewarding and provides great insights into the subject, on the other hand it requires substantial self-study and a willingness to make lots of mistakes and not be frustrated by them.

You are also expected to listen to the ideas of other students and be respectful to them even if you think you have the "correct" solution. The environment of an IBL classroom is collaborative and not competitive and the main goal is to have loads of fun while learning some amazing mathematics.

What does a typical class look like? You come to the class having read the reading assignment and hopefully with lots of questions, we'll discuss your questions first, I'll then hand out the problem sheets which you'll solve in small groups, I'll roam around and help out wherever necessary. You'll not be allowed to use laptops or other electronic devices in class, so you need to bring either a hard copy of the book or more preferably your own handwritten notes to the class.

Homeworks

Homeworks are what make this course. Your homework will consist of three parts:
  • Reading assignments: You will be assigned parts of the book to be read BEFORE every class. These assignments are extremely crucial as there will not be any lectures and you'll be learning the subject by reading the book. You'll not be expected to have understood everything that you've read, but you'll be expected to make good notes and ask questions about it in class. If you skip this step you will likely be completely lost and almost certainly fall behind.
  • Group discussions: This is where most of the magic happens. In class instead of passively listening to a lecture you'll be actively discussing problems with other students and/or the instructor and learning the subject in a very hands-on manner.
  • Writing: You will be required to write the solutions to the problem sets by yourselves. Learning the language of mathematics is a crucial part of the learning process and like any other language you will need a lot of practice to get good at it.
I'll hand out problem sets in each class which you'll discuss in small groups, write the solutions by yourselves and submit them on the following Friday.

Grading Scheme

Class participation : 20%
Homeworks : 40%
Final Exam : 40%

Each week's problem sets count as one homework, only the top 10 homeworks will be included in the final grade.