Transitions, MTH 299-05
Tentative Schedule and Homework Assignments
Chapter numbers refer to:
Chartrand, Polimeni, and Zhang. Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition (2012).
The numbers in the parentheses refer to the corresponding problems in the Second Edition of the book, in case the numbers differ.
| L | Date | Chapter and Topic | HW | Comment |
| 1/6 | Class cancelled | Read Chapter 0: Communicating Mathematics. If you don't have the book yet, read this. |
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| 1 | 1/8 | [1.1] Describing a Set [1.2] Subsets [1.3] Set Operations | Due 01/13:1.1:1.2, 1.4, 1.8 (missing), and 1.68 (1.48) 1.2: 1.12 (1.10) and 1.14 (1.12) 1.3: 1.22 (1.17), 1.26 (1.21), 1.30 (missing) and 1.76 (1.56) | Lecture Notes Supplement for Lecture 1 HW problems from Ch. 1 |
| R | 1/9 | Recitation | ||
| 2 | 1/10 | [1.4] Indexed Collections [1.5] Partitions [1.6] Cartesian Products |
Due 01/15:1.4:1.36 (1.28) and 1.38 (1.26) 1.5: 1.46 (1.32) and 1.50 (1.38) 1.6: 1.59 (1.43), 1.64 (missing), and 1.66 (missing). Exercise 1.66 is a bonus problem. | Supplement for Lecture 2 |
| 3 | 1/13 | [2.1] Statements [2.2] More Implications [2.3] Disjunction and Conjunction | Due 01/17:2.1:2.1, 2.2, 2.4 2.2: 2.14 (missing) 2.3: 2.16 (2.11), 2.18 (2.13) | Lecture Notes HW problems from Ch. 2 |
| 4 | 1/15 | [2.4] Implications [2.5] More Implications | Due 01/22:2.4:2.20 (2.15), 2.24 (Not in v. 2), 2.28 (Not in v. 2) 2.5: 2.32 (2.20), 2.34 (a,b,e,f) (Not in v. 2) | Lecture Notes |
| R | 1/16 | Recitation | ||
| 5 | 1/17 | [2.6] Biconditionals [2.7] Tautologies and Contradictions | Due 01/24:2.6:2.36 (2.25), 2.40 (2.27), 2.44 (2.29) 2.7: 2.46 (2.30) | Lecture Notes |
| 1/20 | MLK Holiday - No class | |||
| 6 | 1/22 | [2.8] Logical Equivalence [2.9] Properties of Logical Equivalence | Due 01/27:2.8:2.52 (2.35), 2.54 (2.37) 2.9: 2.58 (2.39), 2.60 (2.41), 2.62 (Not in v.2) | Lecture Notes |
| R | 1/23 | Recitation | 7 | 1/24 | [2.10] Quantified Statements | Due 01/29:2.10: 2.68 (2.46), 2.70[c,e,f] (2.48), 2.74 (2.50), 2.78 (Not in v.2). | For 2.68 - state the negations of the statements and state original statements in symbols. For 2.70 if you decide that the statement is false, provide a counterexample. |
| 8 | 1/27 | [3.2] Direct Proofs | Due 01/31:3.2:3.8 (3.6), 3.10 (3.8), Problem 3 from here. | Lecture Notes Carefully read Sections 3.1 and 3.2, as well as 3.3 and 3.4 to prepare for next class. |
| 9 | 1/29 | [3.3] Proof by Contrapositive [3.4] Proof by Cases | Due 02/033.3: 3.16 (3.12), 3.21 (3.18), 3.50 (3.36), 3.583.4: 3.2B, 3.4A and 3.4B from the last page of the lecture notes. | You might want to start working on 3.58 early on. HW problems from Ch. 3 |
| R | 1/30 | Recitation | ||
| 10 | 1/31 | [4.1] Proofs Ivolving Divisibility [4.2] Proofs Involving Congruence | Due 02/054.1: 4.2, 4.4, 4.64.2: 4.14(4.10), 4.18(Not in v. 2), 4.22(4.16) | Lecture Notes |
| 1/31 | Last day to withdraw with tuition refund | |||
| 11 | 2/3 | [4.3] Proofs Involving Real Numbers | Due 02/074.3: 4.78(4.66), 4.89(4.65), 4.90(Not in v.2) | Lecture Notes |
| 12 | 2/5 | [4.4] Proofs Involving Sets | Due 02/104.4: 4.43 (4.30), 4.48, 4.50 | For 4.43, for (a) and (b), make sure to present examples different than the back of the book. For (c), note that the proof in the back is not complete - you will need to complete it. HW problems from Ch. 4 Lecture Notes |
| R | 2/6 | Recitation | ||
| 13 | 2/7 |
[4.5] Properties of Set Operations [4.6] Proofs Involving Cartesian Products | Due 02/124.5: 4.56(4.38)4.6: 4.62(4.40), 4.64(4.42), 4.68(4.46), 4.70(4.48) | For 4.68 we proved one of the inclusions in class; for HW prove the remaining one. For 4.70 we discussed one example; for HW provide a different one. You can use finite or infinite sets. Make sure you specify your universal set. |
| 2/10 | Review | Review problems for exam 1 | ||
| 2/12 | Review | Solutions to review problems for exam 1 | ||
| M | 2/13 | Midterm Exam | ||
| 14 | 2/14 | [5.1] Counterexamples | Due 02/195.1: 5.2, 5.4, 5.6, 5.8 | HW problems from Sect. 5.1 Lecture Notes |
| 15 | 2/17 | [5.2] Proof by Contradiction | Due 02/215.1: 5.10(5.7), 5.20(5.17), 5.28, 5.32 | HW problems from Sect. 5.2 |
| 16 | 2/19 | [5.4] Existence Proofs [5.5] Disproving Existence Proofs | Due 02/245.4: 5.405.5:5.50, 5.57, 5.62, 5.65 Bonus: 5.52 | HW problems from Sect. 5.4 and 5.5 Lecture Notes |
| R | 2/20 | Recitation | ||
| 17 | 2/21 | [6.1] Mathematical Induction | Due 02/266.1:6.6b(6.8b),6.14, 6.16, 6.48(6.39) | HW problems from Sect. 6.1 Lecture Notes |
| 18 | 2/24 | [6.2] A More General Principle of Mathematical Induction | Due 02/286.2: 6.24, 6.26, 6.30a | HW problems from Sect. 6.2 |
| 19 | 2/26 | More on induction | Due 3/12Homework problems | Read Section 6.3 |
| 2/26 | Last day to withdraw with no grade reported | |||
| R | 2/27 | Recitation | ||
| 20 | 2/28 | Due 3/10Essay Homework |
Read Chapter 7 | |
| Spring Break | 3/3 - 3/7 | |||
| 21 | 3/10 | |||
| 22 | 3/12 | [8.1] Relations [8.2]Properties of relations [8.3] Equivalence Relations | Due 03/148.1: 8.4 (8.4), 8.6, 8.108.2: 8.12 (8.6), 8.14 (8.8), 8.16 (8.10), 8.22 8.3: 8.24 (8.14) |
HW problems from Sect. 8.1,8.2 Lecture Notes |
| R | 3/13 | Recitation | ||
| 23 | 3/14 | [8.4] Properties of Equivalence Classes [8.5] Congruence Modulo n [8.6] The Integers Modulo n | Due 03/198.3: 8.28, 8.308.4: 8.38 8.5: 8.52 8.6: 8.54, 8.56, 8.58 |
HW problems from Sect. 8.3-8.6 Lecture Notes |
| 24 | 3/17 | [9.1] The Definition of Function | Due 03/219.1: 9.4, 9.8, 9.10, 9.12a,b,d |
HW problems from Sect. 9.1 Lecture Notes |
| 25 | 3/19 | [9.3] One-to-One and Onto Functions | Due 03/249.3: 9.20, 9.63, 9.67c,d, 9.68-bonus, 9.78-bonus |
HW problems from Sect. 9.3 |
| R | 3/20 | Recitation | ||
| 26 | 3/21 | [9.4] Bijective Functions | Due 03/269.4: 9.31, 9.32, 9.34, 9.36-bonus |
HW problems from Sect. 9.4 Lecture Notes |
| 27 | 3/24 | [9.5] Composition of Functions | Due 03/289.5: 9.42a,c, 9.44, 9.46 + example on p.2 in Lecture Notes |
HW problems from Sect. 9.5 Lecture Notes |
| 28 | 3/26 | [9.6] Inverse Functions | Due 03/319.6: 9.54, 9.57, 9.81, 9.83-bonus |
HW problems from Sect. 9.6 Read Sections 10.1 and 10.2 |
| R | 3/27 | Recitation | ||
| 29 | 3/28 | [10.1] Numerically Equivalent Sets [10.2] Denumerable Sets | Lecture Notes | |
| 3/31 | [10.3] Uncountable Sets Review | Due 04/0910.4(10.2), 10.6b(10.14b), 10.10(10.5), 10.20(10.15), 10.22(10.17) | Review problems for exam 2
For 10.4 use 10.3(10.1) as a hint. For 10.22 use 10.25 as a hint. |
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| 4/2 | Review | Solutions to selected review problems for exam 2 | ||
| M | 4/3 | Midterm Exam | ||
| 30 | 4/4 | [11.1] Divisibility Properties of Integers [11.2] The Division Algorithm | Lecture Notes | |
| 31 | 4/7 | [11.3] Greatest Common Divisors | Due 04/1111.1: 11.6, 11.10, 11.1411.2: 11.18, 11.22, 11.26 |
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| 32 | 4/9 | [11.3] Greatest Common Divisors [11.4] The Euclidean Algorithm | Due 04/1411.3: 11.32, 11.34, 11.3611.4: 11.38b, 11.42 |
Lecture Notes |
| R | 4/10 | Recitation | ||
| 33 | 4/11 | Lecture Notes | ||
| 34 | 4/14 | [12.1] Limits of Sequences | Due 04/1812.4, 12.6, 12.8 |
Lecture Notes |
| 35 | 4/16 | Due 04/23Examples 1, 2, 5 on p. 5 and 6 of Lecture Notes |
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| R | 4/17 | Recitation | ||
| 36 | 4/18 | |||
| 4/21 | Review | Final exam review problems | ||
| 4/23 | Review | Selected review problems from FS13 with solutions | ||
| R | 4/24 | Recitation | ||
| 4/25 | Review | Solutions to selected problems from the final exam review | ||
| 4/28 | Extended Office Hours | Room A116 WH | 5:00 pm -7:00 pm | |
| 4/28 | MLC Hours with Ethan | MLC | 6:20 pm -9:50 pm | |
| E | 4/29 | Final Exam 5:45pm - 7:45pm | Room A128 WH |