Analysis

Course: Analysis

Instructor: Mesut B. Çakır, Ph.D.

Important Information & Assignment: See relevant links below.

 

Textbooks

Analysis Textbooks

Course Textbook


Rudin, Principles of Mathematical Analysis, 3ed,McGraw-Hill


Course Textbook
(More friendly)

Abbott, Understanding Analysis, Springer
Protter, Basic Elements of Real Analysis, Springer


Another friendly book

Rosenlicht, Introduction to Analysis, Dover


Rudin's book is a classic but a very hard textbook for the beginner in Mathematical Analysis.  It is written for advanced undergraduate and first year graduate students.  Our goal is to cover all the material in the book, but even I know that this is a very unrealistic goal.  We will try to get as close to this goal as possible.  Therefore, we will make use of Abbott's and Protter's books whenever we can.  [Yes, I know this sounds somewhat illogical; we can't finish one book; therefore, we'll use two more books and will end up finishing threee books instead of one.  However, you might see the logic in this once you start studying the material in the first few chapters of all three books.  They complement each other.]  I will post various documents on this page to ease your struggles with Analysis.

You should check this website at least once a week throughout the year.  I will post various questions for each chapter which should help you understand the material a little better.  I will also post any relevant links I can find to ease your pains.  Such as this one Analysis Webnotes, University of Nebraska

Monthly Assignments
Summer Assignment November February May
September December March June
October January April  


Monthly Assignments
1 Read the whole chapter and get intimidated.
2 Read each section for the second time but in a more focused manner.
  i Restate each theorem, concept, definition, etc. as a question.
  ii Study the proofs, concepts, definitions, etc.
3 Answer each of your questions without the help of the book
  i Check your answers with the book.
  ii But remember that the book's proofs are missing intermediate steps
  iii You should make sure to fill in all the missing steps.
  iv Go back and answer your questions one more time.
4 Study the relevant chapters and sections in Abbott's, Protter's, and Rosenlicht's books.
5 Answer my questions.
  i If you are able to answer more than 90% of my questions correctly, move to Step 6
  ii If not, go back and study the relevant concepts.
  iii Repeat the above steps until you get to 90%, then move to the next step.
6 Tackle the problems in Rudin's book.
7 Repeat these steps with the next chapter.