MA 240, Fall 2007, Instructor: Jeffrey Horn

CLASS ANNOUNCEMENTS (Monday, Dec. 10, 2007)

General Announcements (for all students)
- Added some new homework solutions, specifically for HW4 (Predicate Logic) and HW7 (Combinatorics). I also hung some hardcopies of these on the bulletin board next to my office door (NSF 1119).
What IS New:
- Our final exam will be 4-5:50pm on Tuesday, Dec. 11, 2007, in our usual classroom (NSF 1205).
- HW 8 (Graphs and Trees) was handed out in class (two double-sided pages) on Monday, Dec. 3. Due by the final exam (4pm, Tuesday, Dec. 11, 2007), because that is when (and where!) I will hand out the solution to HW8.
What Was New
- HW 7 (Combinatorics) is assigned below.
- HW 6 (Counting) is assigned and is due BEFORE YOU LEAVE FOR THANKSGIVING! See below.
- HW 4 (2nd Order Logic) is assigned and is due next Wed. (Nov. 7) See below.
- HW 5 (Number Systems) is assigned and is due next Wed. (Oct. 24.) See below.
- Quiz 1, 2-bit BINARY ADDER Truthtable, is due on Monday, Oct. 1, in class (it is take-home). If you missed the handout in class, you can download it here.
- Our first computer science colloquium of this semester will be this Thursday, Sept. 27, at 4pm, in NSF 1205, featuring a visiting faculty from MTU! See here for details...
- Homework 3 (Digital Braitenberg Vehicles) due date is extended from today, Wed., 9-26-07, to Friday, 9-28-07 (so that we can go over an extensive example of the truthtable => boolean expr. => circuit development process, in class on Wed.)
- Scott Raiford's Digital Braitenberg simulator. (If you are interested in trying an Analog Braitenberg Vehicle simulator, try the open-source Breve simulator that some of our students have been using for research.)
- Homework 3 is assigned (Digital Braitenberg Vehicles), see link below (or click here).
- Homework 2 is assigned (in class), and is now on this page; see below.
- The trip to the upcoming Argonne National Laboratory's Symposium for Undergraduates will be Nov. 3-4. The deadline for registration is Friday, Sept. 14, 2007, but if you want to travel with the department group, you will need to give us paperwork by Thursday, Sept. 13. More details to come. Here is a link to the conference info at Argonne: http://www.dep.anl.gov/p_undergrad/ugsymp/
- Homework 1 (assigned in class) is now on this page, below.
- Welcome to class! Please see the syllabus

CONTENTS:

Administrativa
Lecture Notes
Homeworks
Tests and Quizes

ADMINISTRATIVA

LECTURE NOTES 28

Week of August 27 (first week!)
- Introduction, Syllabus, Policies (attendance, etc.)
- Overview of course, topics
- Readings: Chapter 1, sections 1.1 and 1.2
- Intro to Propositional Logic:
  - Propositional Logic <->
Week of Sept. 4. (Labor Day Week)
- Homework 1 due on Friday.
- Go over Prop. Logic topics:
  - Truth tables
  - Compound boolean expressions
  - Proof by truth table

HOMEWORKS

HOMEWORK 1: Propositional Logic
- HANDED OUT: (in class) Friday, Aug. 31, 2007
- DUE ON: Friday, Sept. , 2007 IN CLASS! (solution will be handed out on Friday, in class, so no late hand-ins will be accepted for HW1!)
- First read sections 1.1 and 1.2 of Rosen
- Then do problems:
  - pp. 16-18 of Rosen text: #8 (all), # 28 (all), #40.
  - Extra Credit: Two-roads, two people (liar and truthteller), one question (in class)
HOMEWORK 2: Boolean Algebra
- HANDED OUT: (in class) Monday, Sept. 10, 2007
- DUE ON: Monday, Sept. 17, 2007
- First read sections 10.1 and 10.2 of Rosen (can skip subsection on topic of "Duality")
- Then do problems:
  - pp. 707-708 of Rosen text: 2, 4, 6, 8, 10, 22, and 30.
  - EXTRA CREDIT: (the question on the Extra Credit solution for HW1)
HOMEWORK 3: Digital Braitenberg Vehicles (click here)
HOMEWORK 4: 2nd Order Logic (the Predicate Calculus)
- HANDED OUT: (in class) Monday, October 29, 2007
- DUE ON: Wednesday, November 7, 2007
- First read sections 1.3 and 1.4 of Rosen
- Then do problems:
  - pp. 40-44 of Rosen text: # 6 (all parts, and indicate WHICH are logically equivalent to which others), 34, 54.
  - pp. 51-56: #6 (any two), #10, #30.
- SOLUTION
HOMEWORK 5: Number Systems
- (click here; this is the two-page (double-sided) handout I gave in class Wed. Oct. 17.)
- Also, here is an additional page from the 3D Game Studio manual that has some additional background information for Question 10. Just background info!
HOMEWORK 6: (Counting)
- HANDED OUT: (in class) Wednesday, Nov. 14, 2007
- DUE ON: Before Thanksgiving break!
- First read section 4.1 of Rosen
- Then do problems:
  - pp. 310-312 of Rosen text: #8, 12, 14, 48.
  - AND the QUADRAPOD question:
    - How many different QUADRAPOD GAITS are possible?
    - Imagine that we want to do work similar to what Gary Parker did in the 1990s on hexapods, but we want to work on quadrapods (or quadrapeds). That is, we want to use artificial evolution, working in a simulator (e.g., the Breve system, see below, middle image), to try to evolve walking gaits for a 4-legged robot.
    - Definitions:
      - Each servo motor can be commanded to go to a specific position (with a 180 degree range, FYI) with a single byte number. That is, eight bits of information. This means that each servo motor can be in any of 2⁸ = 256 different positions.
      - Each leg has TWO servos that move independently. One is for vertical movement of the leg, and the other is for horizontal. This means they are mounted perpendicular to each other, which means that the effect of the their movements on the position of the foot are INDEPENDENT. So each COMBINATION of the two servo motor positions yields a unique LEG POSITION.
      - Each robot has four legs, which of course move independently. Each combination of four different leg positions yields a unique STANCE.
      - A GAIT consists of a repeated sequence of ten (10) consecutive stances. So any (and all) combination often stances (can include repeats) we define as a unique gait.
    - QUESTIONS:
      1. How many unique GAITS are possible? Show your work for partial credit, particularly by showing the following intermediate results: number of unique LEG POSITIONS for a single leg, number of unique STANCES, and finally, number of unique GAITS.
      2. Lynxmotion now makes a Quadrapod with THREE degrees of freedom (that is, three servo motors) per leg, for a total of twelve servos. (See below, right image.) That's a lot to control! Let's assume that the three servos can be mounted so as to be completely independent of each other, so that each combination of three servo positions yields a unique leg position. How many 10-stance gaits are possible with the 3-DOF hexapod?
HOMEWORK 7: (Combinatorics)
- HANDED OUT: (in class) Monday, Nov. 26, 2007
- DUE ON: Monday, Dec. 3, 2007 (No late homeworks this time!)
- First read section 4.3 of Rosen
- Then do problems:
  - pp. 324: #1, 2, 6, 10, 20, 22 (a,b,c ONLY), 34, and 40 (extra credit).
  - (note: the problems go from very easy to quite hard! So go through them in order, and be certain to get all of the easier points, by being careful to answer the right question and to read all the directions! Also, don't forget the "custom" problem below, which is NOT extra credit!)
  - ALSO:
    - Look at question 33 on page 334 (answer is on page s-36)
    - Also, look at your class notes.
    - Then answer these questions about the following map:
    - Students going to the university from the subway stop are always in a hurry and so they will only go either east or south, never north or west. Therefore, they will always have to travel five blocks east and five blocks south, for a total of ten blocks, but in many possible combinations. But never will students enter "DarkWood", which is a city park that has become populated by hideous and evil creatures (for some unknown reason). Sarah, an NMU alumna, has started her own coffee house business, StarDoe, which she has located at the intersection marked by the green star above. Assuming that students going from the subway stop to the university each morning are equally likely to take each of the possible paths (of those that do NOT go THROUGH DarkWood; they can skirt the edges, however), Sarah wants to know what percentage of those students will go through her intersection.
      1. How many shortest paths (8 blocks) exist?
      2. At her current location (green star), how many of these shortest paths (of exactly eight blocks) go through her intersection?
      3. Sarah has the possibility to relocate to either of the two white star locations above. Which, if either, would give her more people traffic?
    - SOLUTION

TESTS AND QUIZES

Quiz 1, 2-bit BINARY ADDER Truthtable, is due on Monday, Oct. 1, in class (it is take-home). If you missed the handout in class, you can download it here.