- I've approved some more projects, but lots remain unknown. If you have your proposal on paper, please hand it in; if not, please send me an email of your "intent to stress".
- Midterm exam:
- Key -- to come
- Max:
- Average: 77
- Median: 77
- Distribution of grades:
90s 80s 70s 60s < 60s 5 9 8 7 3 - You may "repair" any one problem for half the missing
points. Those are due (attached to your original exam) by
Thursday.
- Also, feel free to discuss your exam and/or your situation with me outside of class.
- Midterm grades: were calculated assuming that your final exam
grade will be the same as you midterm grade; that your project
will be so well executed that you get 100%; and I dropped your
two lowest quiz scores to compute your quiz average.
- Quiz Thursday will be over section 4.1
- We got pretty well through Section 4.1 (Sets).
- One focal point was the analogy between the binary operations of
logic ($\land$ and $\lor$) and the binary operations of sets ($\cup$
and $\cap$).
- The power set was the primary tool we encountered, and we saw how
it might be used in Venn
diagrams to describe how many different subsets one can make with
two sets in a universe.
It is also the tool by which we come to the realization that infinity comes in various sizes....
- One focal point was the analogy between the binary operations of
logic ($\land$ and $\lor$) and the binary operations of sets ($\cup$
and $\cap$).
- We begin with a proof that infinity comes in many sizes.
- Then we will work on Section
6.1 (Graphs).
As we prepare to investigate graphs, we might think about this recent example, from Science: Gigantic map of fly brain is a first for a complex animal: Fruit fly 'connectome' will help researchers to study how the brain works, and could further understanding of neurological diseases.
This "map shows all 3,016 neurons and 548,000 synapses tightly packed in a young Drosophila's brain, which is smaller than a poppy seed."
- From the 6.2 highlights:
- Handout: terminology and Fibonacci example
- Tree problems
- Josh Werrman's brute force solution to Will Short's puzzle.
- Fibonacci numbers via a fractal tree
- Example 24, p. 513
- Sights and sounds of Tree traversal
- Reverse Polish Notation
- How many unique binary search trees?
- Graph Terminology Handout
- Tree Terminology Handout
-
If you check out this code, you'll see where I compute the power set ("all-subsets") of a set, to cover all the bases. I think that the end result is pretty beautiful, too!
- Recursive in-order, post-order, pre-order in lisp
- Recursive computation of Fibonacci numbers (in lisp)
- Recursive computation of rows from Pascal's triangle (in lisp)
- "String exponention" (in lisp)
- Here is the recursive selection sort algorithm, in lisp:
- Here is a recursive binary search algorithm in lisp:
- Closed-form computation of Fibonacci numbers (in lisp)
- Some examples of the Euclidean algorithm:
- Simple and clean recursive Euclidean Algorithm in lisp:
- Written as a while loop, using the recurrence relation:
- Here is a recursive bubbleSort algorithm in lisp
(coded up following our author's algorithm, in section 3.3, p. 214, as closely as possible).
