All ISU undergraduate students are invited to participate in the Problem of the Week Contest.
| MONTH WEEK | DAY | Topics, Reading Assignment | Practice Problems | Assigned Problems, Due at 2nd following class |
|---|---|---|---|---|
| January | ||||
| Chapter 1: Numbers, Sets, and Functions | ||||
| WEEK 1 | 10-14 January | |||
| Mon 10 | Course Introduction Communicating Mathematics Sets | 1.33, 1.34, 1.38 | 1.32 | |
| Wed 12 | Functions, Inverse image and level sets | 1.45, 1.49 | 1.51 | |
| Fri 14 | The Real Number System Fields | 1.52-1.54 | ||
| WEEK 2 | 17 - 21 January | |||
| Mon 17 |  Martin Luther King Day Holiday No class meeting | |||
| Wed 19 | The Real Number System Ordered Fields | |||
| Fri 21 | The Real Number System Completeness | In-class Exercises page 17: 1.43 Proposition (g) 1.44 Proposition O2 1.45 Proposition F2 1.46 Proposition (a) | 1.55 | |
| WEEK 3 | 24 - 28 January | |||
| Chapter 2: Language and Proofs | ||||
| Mon 24 | Theorems about equations Quantifiers, Statements | 2.1, 2.2, 2.4 | 2.16 | |
| Wed 26 | Order of quantifiers Negation of quantified statements | 2.9, 2.10, 2.19, 2.28 | 2.22 | |
| Fri 28 | Compound statements | 2.37, 2.38, 2.44 | 2.48 | |
| WEEK 4 | 31 January - 4 February | |||
| Mon 31 | Techniques of proof | 2.51(a) | ||
| February | ||||
| Wed 2 | ... continued | |||
| Fri 4 | In-class Exercise: REVIEW of Chapters 1-2 | 1.49(a),(c), 2.52, and Prove: If x is even then x+1 is odd.
| ||
| WEEK 5 | 7 - 11 February | |||
| Mon 7 | FIRST MIDTERM EXAM Covers Chapters 1-2. Objectives for 1st midterm exam. | |||
| Chapter 3: Induction | ||||
| Wed 9 | The Principle of Induction | 3.2, 3.3, 3.11 | 3.5 (Prove by induction.) | |
| Fri 11 | 3.14(a),(d), 3.16 | 3.15 | ||
| WEEK 6 | 14 - 18 February | |||
| Mon 14 | Applications of Induction | In-class Exercise: Binomial Coefficients | Prove the factorial formula,
Theorem 3 for binomial coefficients. Extra Credit: Write up a proof of Theorem 2 on subset counting. | |
| Wed 16 | (Applications, continued) | 3.20, 3.23, 3.28 | 3.22 | |
| Fri 18 | Strong Induction | 3.55 | 3.56 | |
| WEEK 7 | 21 - 25 February | |||
| Chapter 4: Bijections and Cardinality | ||||
| Mon 21 | q-ary representation of integers | 4.1, 4.16 | 4.15 | |
| Wed 23 | Bijections | 4.21 | 4.22 | |
| Fri 25 | Injections & Surjections Composition of functions | 4.23, 4.24, 4.25 | 4.30 | |
| WEEK 8 | 28 February - 4 March | |||
| Mon 28 | Cardinality -- finite sets | 4.33, 4.35, 4.36 | 4.34 | |
| March | ||||
| Wed 2 | Cardinality -- infinite sets
Read about The
Hilbert Hotel | 4.42, 4.43, 4.47 | 4.45 (Due Wednesday, 9 Mar) | |
| Fri 4 | REVIEW of Chapters 3-4 | In-class Exercise: 3.31, 4.3, 4.27, 4.31 | ||
| WEEK 9 | 7 - 11 March | |||
| Mon 7 | SECOND MIDTERM EXAM Chapters 3-4. Objectives for 2nd midterm exam. | |||
| Chapter 13: The Real Numbers | ||||
| Wed 9 | Completeness | 13.8, 13.13, 13.22, 13.24 | ||
| Fri 11 | Archimedean property | 13.19 | ||
| 14 - 18 March: WINTER RECESS | ||||
| WEEK 10 | 21 - 25 March | |||
| Mon 21 | Limits | 13.11, 13.26, 13.27, 13.28 | 13.25 | |
| Wed 23 | Monotone Convergence | 13.29, 13.31, 13.32 | 13.30 | |
| Fri 25 | k-ary representation of real numbers | 13.14, 13.33, 13.34 | 13.36 | |
| WEEK 11 | 28 March - 1 April | |||
| Mon 28 | Uncountability | 13.6, 13.37 | 13.38 | |
| Chapter 14: Sequences and Series | ||||
| Wed 30 | Convergent sequences | 14.3, 14.9, 14.10, 14.13, 14.14, 14.17, 14.19 | 14.15 | |
| April | ||||
| Fri 1 | Sequence limit properties | 14.22 [HINT: Lemma 3.13] | ||
| WEEK 12 | 4 - 8 April | |||
| Mon 4 | Cauchy's convergence criterion | 14.29 | 14.31 | |
| Wed 6 | Bolzano-Weierstrass Theorem | 14.30 | 14.28(b) | |
| Fri 8 | Infinite Series | 14.6, 14.12, 14.33, 14.36, 14.38, 14.49 | 14.45 | |
| WEEK 13 | 11 - 15 April | |||
| Mon 11 | Convergence tests for Series | 14.46, 14.58, 14.61, 14.63 | 14.52. For full credit, prove (a) or (b). For double credit, prove both (a) and (b). | |
| Chapter 15: Continuous Functions | ||||
| Wed 13 | Limits and Continuity | 15.1-3, 15.6, 15.8, 15.15, 15.18 | ||
| Fri 15 | Limits and Continuity, continued | 15.12 | ||
| WEEK 14 | 18 - 22 April | |||
| Mon 18 | Intermediate Value Theorem | 15.4, 15.7, 15.22, 15.24, 15.30, 15.33 | 15.23 | |
| Wed 20 | Maximum-Minimum Theorem | 15.9-10, 15.26 | 15.9(d) | |
| Fri 22 | Uniform Continuity | 15.35(b) | ||
| WEEK 15 | 25 - 29 April | |||
| Mon 25 | REVIEW Chapter 13 | 13.8, 13.11, 13.14, 13.29 | ||
| Wed 27 | REVIEW Chapter 14 | 14.6, 14.10, 14.33, 14.35(b) | ||
| Fri 29 | REVIEW Chapter 15 | 15.4, 15.10, 15.14, 15.18(b) | ||
| May | ||||
| FINAL EXAM WEEK | 2 - 6 May | |||
| Wed 4 | FINAL EXAM 2:15 - 4:15 p.m. Objectives for Final Exam
| | ||
