Topics to be covered in Midterm I:


-Sequences 

-Limits: neighborhoods and tails, epsilon definition

-Working with specific sequences: finding limits from definition, estimates, limit laws

-Properties of convergent sequences: uniqueness of limit, convergent sequence is bounded, etc

-Infinite limits, properties of sequences diverging to infinity

-Limit Laws (and their versions for infinite limits, when applicable

-Bounded sets and sequences, upper/lower bounds, supremum and infimum, completeness axiom

-Theorem: monotone bounded sequence converges

-series and their properties (as detailed in posted lecture notes and in homework 6)

-subsequences: definition, finding subsequences with certain properties. 
 Theorem: if a sequence converges, all its subsequences converge to the same limit.

-integers, rationals, algebraic and order axioms for rationals and reals. 
 (This topic will not be emphasized. You need not memorize the axioms, 
  but you should be able to derive simple statements from the axioms by using logic)

    
For a more detailed description of the material, see reading assignements for each week and the homework. 
You are responsible for all the material covered in the lectures as well as the homework. 

The best exam preparation is to make sure you understand everything in the lectures and 
know how to do each question in the homework, as well as similar questions.

Some extra practice questions from the textbook: 
3.3, 3.4, 4.1-4.4, 4.8. 4.9, 7.4, 8.2, 8.3, 8.5, 8.8, 8.9, 
8.10,  9.1, 9.3, 9.9-9.12, 10.1, 10.2, 10.7.