Math 8a, 2019-20

Homeworks

These homeworks are copyrighted material, posted here for use by SchoolNova students and parents. Everyone else is welcome to print a copy of these materials for their personal use; any redistribution or commercial use is prohibited

• Assigned on 09/15: Review Problems, mostly for combinatorics  |  
  
• Assigned on 09/22: Pascal's Triangle  |  
  
• Assigned on 09/29: Combinatorics Sheet 3: Formula for nCk  |  
  Please do all the problems before the New York State lottery problem, except for the problem about five-letter words; beyond that, please attempt one more combinatorics problem, and one of the miscellaneous problems. As always, if you wish to do more, please do, I will look at everything you submit.
  
• Assigned on 10/6: Combinatorics Final: Binomial Theorem: Binomial Theorem and its uses  |  
  Please do problems 1-6; of the remaining problems 8-10 and Miscellaneous 1-3, please choose one of the six to do. Additionally, please consider registering for the AMC Competition if you are interested! The registration link is in an announcement, viewable from the schoolnova website homepage.
  
• Assigned on 10/20: Logic 1: Links!: An Introduction to Abstract Thinking  |  
  
• Assigned on 10/27: Logic 2: Introduction to Symbolic Logic  |  
  Please do problems 6-12.
  
• Assigned on 11/3: Logic 3: Laws and Proofs  |  
  Hello! Please work through problems 1-5 at least, and then choose whatever you want from the remaining problems
  
• Assigned on 11/10: Logic 4: Proof Techniques  |  
  Please attempt any five of the problems on this homework! :)
  
• Assigned on 11/17: Math Battle!: Fall Challenge Problems With Solutions  |  
  
• Assigned on 11/24: Logic 5: Quantifiers  |  
  
• Assigned on 12/8: Logic Review: Statements, Quantifiers, Iff, Contradiction  |  
  
• Assigned on 12/15: Review: Past Problems  |  
  These are mostly all problems from past homework sheets, so not much you haven't seen before. The exception is problem 10, which is not a problem we proved or discussed in class. Work through any of these problems that you didn't get a chance to do in past weeks, and try number 10 if you want a challenge.
  
• Assigned on 01/5: Elephants and Hamsters: An Axiomatic Theory  |  
  As there are less of us in class now, I decided we can try something a little more dynamic, so here I introduce you to the Elephants and Hamsters theory. This is a fun little study in axiomatic theory, and includes some rather nontrivial, sometimes difficult, combinations of the axioms in order to solve the problems. Look through the sheet, and attempt problems under the "Practice Problems" section. Solving these problems will require you to keep careful track of what you are talking about, and to be able to distinguish the different categories (Elephants, Hamsters, theme songs) so that you be able to understand how to simultaneously work with objects that have different properties.
  
• Assigned on 01/12: Euclidean Geometry 1: Axioms, Postulates, and Triangles  |  
  I've changed the style of the homeworks - problems are now all approximately equal in difficulty, and I want each of you to prepare to present one of them the next week
  
• Assigned on 01/19: Euclidean Geometry 2: Circles and Right Triangles  |  
  
• Assigned on 01/26: Euclidean Geometry 3: Triangle Inequalities, Special Lines, Construction  |  
  
• Assigned on 02/2: Euclidean Geometry 4: Quadrilaterals  |  
  
• Assigned on 02/9: Euclidean Geometry 5: Circles and Inscribed Angles  |  
  
• Assigned on 02/23: Euclidean Geometry: Additional Problems  |  
  
• Assigned on 03/1: Last Day of Geometry: Review & Logic Refresher Problems  |  
  As we ended our geometry unit today, I have assigned some problems to get you back in the habit of working with formal logical language. I definitely want you to attempt at least the first three logic problems; take a look at the rest of the problems on this sheet as well, if they interest you. Don't be turned off by long paragraphs - formal logic requires reading comprehension, so I expect you to read what I write for you in these problems.
  
• Assigned on 03/8: Number Theory 1: Factors, Primes, Greatest Common Divisor  |  
  Our first week of number theory! The introductory concepts may be ones you have heard of before - they concern divisibility and factors, including things like prime numbers and gcd (greatest common divisor). That said, we will derive all of our information from these definitions plus algebra basics (manipulating equations) and logic (that we developed last semester), so you need to know how to work with these definitions and follow the proofs of the theorems. You should spend some time on this sheet, as these fundamentals will be important.
  
• Assigned on 03/22: Number Theory 2: Euclid's Algorithm  |  
  
• Assigned on 03/29: Number Theory 3: Prime Factorization  |