Math 310

Spring 2011

Miniprojects

The following is a long list of what I am calling "Miniprojects".  These are problems that are intended to be interesting, fun, and perhaps challenging, and might also preview later topics in this or other courses in Math or Computer Science.  Some of the topics are just fun and games, some are very mathematical, and a few are very applicable to computer science, so your interest level in each miniproject will vary depending on your own personal interests and on what you want to get out of this course.  Therefore, I do not expect you to do every one of these miniprojects (although you certainly may if you wish!).  The "Miniproject" component of your grade will consist of the best two scores you get on the miniprojects that you submit for each of the six blocks of material, and the next best eight scores overall.  Each of the six blocks of material is determined by the content on each of the five regular exams and the material between the fifth exam and the final.  A total of twenty miniprojects will be counted towards your grade.  Note that there are over eighty available miniprojects for you to choose from over the course of the semester.  You may do as few as twenty miniprojects if you wish, or you may do all of them, or any number in between.  This also means that if you do poorly on some of them, you may do extras to replace the poor score, although at least two scores will be kept from each block of material.  If you want to minimize your work for the end of the semester, you are free to do the eight "freely chosen" miniprojects in the first part of the semester.

I intend for this part of your grade to pique your interest, be at least a little enjoyable, and to help your grade overall.  However, in order for that to occur, you do have to keep up.  I would expect each one to take anywhere from thirty minutes to complete to a couple of hours, depending on your interest, prior knowledge, and sometimes creativity.  But this means that you won't be able to do all of your projects in the last week of the class, at least not if you wish to pass any of your final exams.  This is the reason that I have instituted due dates.  The miniprojects for those sections covered on an exam will be due the class day after the exam.  For example, Exam 1 will be on Friday, January 28 and I expect it to cover sections 1.1-1.3.  Therefore, any of the miniprojects from sections 1.1, 1.2, 1.3 will be due on Monday, January 31.  I chose this for the due date because you would otherwise have little to do (for this class anyway) at that time.  However, to make the most efficient use of your time I would suggest that you look at the miniprojects for the sections as we finish the section, and do any that you like immediately.  You may turn in the miniprojects early if you finish them early (I am not likely to grade them early, but I do promise not to lose them!).  There will be five exams, so this will break the miniprojects into six chunks.  A good rule of thumb is to do at least five miniprojects per exam.  This will cover the minimum of two, the average of one to two of the "freely chosen" ones per exam, and a spare in case of a bad grade.  Note:  The miniprojects for the material between the fifth regular exam and the final exam are due on Study Day, May 4.  I chose this date because I want to be able to return the projects to you with their grades before the final exam.  I will do my best to have these miniprojects graded by 2pm on Friday, May 6, if you want to pick them up before the final exam on Monday, May 9.

Your solutions must include a printout of the problem (or at least the first page) as a cover page, so that I know which one you are doing, and should be well-written and legible.  If your handwriting is atrocious, this means that you might want to type them, but I do not require that they be typed, only neat and legible.  My guess is that it will be rare for you to turn in your initial work - you will most likely have to clean up the scratch work, dead ends, etc. for a copy that is appropriate for grading.

Recap:

    Do at least 20. 

Minimum requirement is at least two per exam.

Minimum goal is at least five per exam.

Extras will replace low scores, with at least two counting per exam.

Two will count per exam, and then the next best eight overall, for a total of twenty miniprojects.

    Due the day after the exam on the relevant section.

    Well-written, legible solution (not just an answer).

    Include a printout of the miniproject statement.

Projects: 

Section 1.1 - Coins Logic problem (note:  You need to write out a solution, not just give the answer.  See the handout for #65 for an example.)

Section 1.1 - Books Logic problem (note:  You need to write out a solution, not just give the answer.  See the handout for #65 for an example.)

Section 1.1 - Body Shop Logic problem (note:  You need to write out a solution, not just give the answer.  See the handout for #65 for an example.)

Section 1.2 - NAND

Section 1.2 - NOR

Section 1.3 - Lewis Carroll (Note:  You may submit this project two times if you wish.)

------------------- Sections 1.1-1.3 above are due on Monday, January 31 -----------------

Section 1.4 - Properties of Real Numbers

Section 1.4 - Prenex normal form

Section 1.5 - Formal Proofs with Quanitfiers

Section 1.5 - Formal Proofs of some Rules of Inference

Section 1.5 - More Formal Proofs of some Rules of Inference

Section 1.5 - Logical Arguments

Section 1.5 - Descartes does not think

Section 1.6 - Some Proofs

Section 1.6 - TFAE Proof

Section 1.6 - Coin Game

Section 1.6 - Finding Errors 

Section 1.7 - 3x+1

Section 1.7 - Bits in a Circle

Section 1.7 - Blackboard Odd

Section 1.7 - Domino Tiling

Section 1.7 - Tetromino Tiling

Section 1.7 - Chomp

Section 1.7 - O'Ekaki

----------------Sections 1.4-1.7 above are due on Thursday, February 17 ---------------------

Section 2.1 - Well-defined Sets

Section 2.1 - Four-set Venn Diagram

Section 2.2 - Symmetric Difference of Sets

Section 2.2 - Multisets

Section 2.2 - Fuzzy Sets

Section 4.1 - Tilings A

Section 4.1 - Tilings B

Section 4.1 - Chomp

Section 4.1 - Modular Arithmetic

Section 8.1 - Irreflexive, Asymmetric, Complements, Inverses

Section 8.1 - Properties With a Concrete Example

Section 8.1 - Reflexive/Irreflexive and Combined Relations

Section 8.1 - Symmetry of Rn

Section 8.3 - Complements and Inverses

Section 8.3 - Properties Galore!

Note:  This miniproject is worth up to four miniprojects.  See the project description.

Section 8.5 - Partitions and Refinements

Section 8.5 - Cat and Mouse

Section 8.5 - Divisibility

Section 8.5 - Feeding the Monkeys

Section 8.5 - Magic Number Squares

----------------Sections 2.1-8.5 above are due on Monday, March 7---------------------

Section 8.6 - Partial Orderings and Cartesian Products

Section 8.6 - Dense Partial Orderings

Section 9.1 - MSUM Buildings

Section 9.1 - NSIC Football

Section 9.2 - Conjecture on Degrees

Section 9.2 - Regular Graphs

Section 9.3 - Adjacency/Incidence Matrices

Section 9.3 - Isomorphic Graphs

Section 9.4 - Strong/Weak Connectedness

Section 9.4 - The Farmer, the Wolf, the Goat, and the Cabbage

----------------Sections 8.6-9.4 above are due on Thursday, March 31---------------------

Section 9.5 - Euler Circuits and Paths

Section 9.5 - Euler/Hamiltonian Circuits and Paths

Section 9.5 - Knight's Tour

Section 9.6 - Your Own Personal Weighted Graph

Section 9.6 - Shortest Paths

Section 9.6 - TSP by Brute Force

Section 9.6 - TSP by Other Algorithms

Section 10.1 - Eccentricity, Center, and Fibonacci

Section 10.1 - m-ary Trees

Section 10.1 - Trees and Forests

Section 10.3 - Binary Arithmetic Trees

Section 10.3 - Postfix Notation

Section 10.4 - Spanning Trees by Brute Force

Section 10.4 - Distances Between Trees

Section 10.5 - Different Spanning Trees

Section 10.5 - Women's Professional Soccer

----------------Sections 9.5-10.5 above are due on Monday, April 18 ---------------------

Section 11.1 - Formal Proofs of Boolean Algebra Results

Section 11.1 - Associative Property

Section 11.2 - Maxterms and Product-of-Sums

Section 11.2 - Sum-of-Products

Section 11.3 - Light Switch

Section 11.3 - Binary Comparison

Section 11.3 - Binary Multiplication

Section 3.6 - Representation of Integers in Other Bases

Section 3.6 - Euclid's Algorithm

Section 3.6 - Multiplication in Other Bases

Section 11.4 - Karnaugh Maps

Section 11.4 - Quine-McClusky

Section 11.4 - Six-Variable Karnaugh

Section 11.4 - Don't Care Karnaugh

----------------Sections 3.6 and 11.1-11.4 above are due on Wednesday, May 4 (to my office) ---------------------

 

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