Material Covered

1. Intermediate Java: 10-20%:
   • Exceptions

   • Interfaces and abstract classes
   • Generics, Casting
   • Iterators
   • Miscellaneous Java programming tidbits, including inheritance
   • Additional material on object-oriented design if time allows.

2. Data structures and Abstract Data Types: 30-50%
   • Recursion
   • Lists, Stacks and Queues
   • Lists and Iterators
   • Maps and Dictionaries

3. Algorithm analysis: 5-15%

4. Discrete Structures (Mathematics): 35-55%
   • Induction
   • Sets
   • Functions and relations
   • Propositional and Predicate Logic, if time allows
   • Methods of proof, if time allows
   • Elementary number theory and cryptography, if time allows

   • Brief introduction to graphs if time allows

Note: the above is a listing of the topics by categories, not the order in which we will cover them. The point off our UIC sequence of Data Structures and Discrete Mathematics I and II is to integrate some of these topics.

So here is my planned organization of this material, subject to change:

1. Selected Java topics
   • Review of arrays (Goodrich, Chapter 1.5)
   • Exceptions (Goodrich, Chapter 2.3)

2. Induction and Recursion (Goodrich, Chapter 3.5 and Bender, Unit IS: Induction, Sequences and Series, Section 1.)
3. Analyzing the running times of programs (Goodrich, Chapter 4).

4. Lists, stacks, and queues
   • Interfaces, Abstract classes, Generics (Goodrich, Chapter 2.4-2.5)
   • Linked lists, stacks, and queues. (Goodrich Chapters 3.2-3.4 and 5.)

   • Lists and Iterators (Goodrich Chapter 5), may skip or compress.
5. Sets, functions, and relations. (Bender, Unit SF: Sets and Functions and perhaps Section 1 of Functions from the second Bender book for some advanced material; also the first section of the Lists chapter of the second Bender book may be useful here to contrast sets and lists.)
6. Maps, dictionaries, and hashing. (Goodrich, Chapter 9.1-9.3).

7. As time allows at the end, selections from:
   • Boolean Functions (Bender, Unit Boolean Functions, Section 1.)
   • Logic (Bender, Unit Logic)
   • Number theory and cryptography (Bender, Unit number theory and cryptography)
   • Basics of graphs and trees (Bender, second book, Unit Graphs Sections 1 and 3).

Our first topic will be Java, but our second topic will be an integrated unit on recursion and proof by induction.