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Stanford MATH 112 - Study Questions

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Math 112-40, Mr. ChurchStudying for the finalTopics covered (page 1) and study questions (page 2)Topics coveredThese are the sections of the book that we have covered in this course.• Section 1.1: Numbers, Sets, and Functions• Section 1.2: Rules of Arithmetic (Axioms for a Ring)• Section 1.3: Even-Odd Arithmetic [Z2]• Section 1.4: One’s Digit Arithmetic [Z10]• Section 2.1: Consequences of the Rules of Arithmetic [theorems about rings]• Section 2.2: Inequalities and Order• Induction• Section 3.1: Divisibiliy• Section 3.2: Greatest Common Divisor• Section 3.3: Primes• Section 4.1: The Division Algorithm• Section 4.2: The Euclidean Algorithm and GCDs• Section 4.3: The Fundamental Theorem of Arithmetic [prime factorization]• Least Common Multiples (part of Section 5.2)• Section 6.1: Congruences• Section 6.2: Groups• Groups of units; units modulo m• Section 7.1: Divisibility Tests• Section 7.3: Check Digits (ISBNs)• Section 8.2: Infinity [sizes of sets, countability]1Study questionsI have selected certain questions from the textbook which would be good to study.This is just a rough guide to which questions are especially worth reviewing. The finalis cumulative, so the list includes questions from all the chapters we have covered.Good. These questions would be good ones to study; these are questions that didnot previously appear on this list.• Chapter 1: 6, 21, 22, 24• Chapter 2: 9, 15• Chapter 4: 8, 13, 20• Chapter 6: 6, 13, 14, 16, 17, 18, 19, 21, 29, 30, 31, 37• Chapter 7: 1, 10, 11Still good. These questions appeared on this list before, but are still good to review.• Chapter 1: 9, 10, 11, 13, 16, 17, 19, 20• Chapter 2: 1, 2, 4, 10, 11• Chapter 3: 2, 7, 8, 10, 11, 12• Chapter 4: 1, 3, 4, 6, 12, 23• Chapter 5: 1, 20, 21• Chapter 6: 5, 7OK. It wouldn’t hurt to look at these questions, but it’s not imperative. (In somecases this is because the question is now standard for us.)• Chapter 1: 3, 4, 5, 7, 12, 14, 15, 28, 30• Chapter 2: 7, 12, 13, 14• Chapter 3: 9, 16• Chapter 4: 14, 15, 17, 18• Chapter 6: 1, 2, 3, 4, 12Practice problems. Most practice problems are useful, because you can compareyour answer with the solution in the book. These are the ones I think are most useful.(New questions are bolded.)• Chapter 1: 4, 7, 8, 10, 18, 22• Chapter 2: 2, 3, 4, 5, 6, 7• Chapter 3: 1, 3, 4, 5• Chapter 4: 1, 3, 4• Chapter 5: 8• Chapter 6: 6, 8, 9, 11, 12• Chapter 7: 2• Chapter 8: 4, 5Note regarding axioms and theorems. On the final, I will provide a sheet listingall the axioms for a ring, the order axioms, and the axioms for a group (together withthe definition of each axiom), and also the Theorems from Chapter


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