'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.
Ch.23: Read statements and proofs of the 4 comparison tests on pages Pg.467-472.
Ch.23: Read the definition of Absolute Convergence and statements of Theorems 5-9. You can skip the proofs of these Theorems.
Instructions for the final: You should think of the final as an excuse to review the fundamentals. You should revise the following topics. It should be enough to go over your own HW solutions to the relevant problem sets.
How to prove continuity/discontinuity of a function using the ε-δ definition,
Intermediate value theorem and it's proof (inf, sup etc.)
Basic computations, Mean value theorem
Critical points , min/max problems
Computing Taylor series, estimating errors
Computations only (substitution tricks, by parts, trig subs etc.)
The exam will mostly consist of self contained problems (you do need to remember all the definitions and theorems) and you'll be graded on logical correctness, there will be very little credit for the 'final answer'.
You have an option of doing a project in this course. If you do choose to do a project I'll reduce the weight of the final exam for you. The project will consist of some independent reading by you about
anything even vaguely related to calculus. Here are a few possible topics for the projects:
Construction of reals, axiom of choice etc.
Pathological functions, nowhere differentiable function, space filling curves etc.
Compactness, Heine-Borel theorem etc.
What is a measure?
You are free to come up with your own topics, these are merely suggestions.
For the project you'll have to submit a written report at the end of the semester. The report should have a rigorous definition-theorem-proof structure.
MW 1:30-2:45pm, Hodson 315
F 1:30-2:20pm, Maryland 217
anakade1 at jhu ddott edu
Calculus, 3rd Edition, Spivak
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 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
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.
Each week's problem sets count as one homework, only the top 10 homeworks will be included in the final grade.