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 |
|---|---|---|---|---|
| August | ||||
| Chapter 1: Writing Proofs | ||||
| WEEK 1 | 9-13 January | |||
| Mon 20 | Course Introduction Conditional Statements, Field axioms | §1.1 #1,3 Fields intro: [Postscript] [Acrobat] | ||
| Wed 22 | Division algorithm; Constructing direct proofs. | §1.2 #1-3 | Fields I: [Postscript] [Acrobat] | |
| Fri 24 | Statements, Logical operators | §2.1 #1-5,9 | §2.1 #6 | |
| Chapter 2: Logical Reasoning | ||||
| WEEK 2 | 27-31 August | |||
| Mon 27 | Logically equivalent statements | §2.2 #3,5,8 | Fields II: [Postscript] [Acrobat] | |
| Wed 29 | Predicates, Sets, Quantifiers | §2.3 #1,2,6 | Fields III: [Postscript] [Acrobat] | |
| Fri 31 | Quantifiers and Negation | §2.4 #2(b),(d),(f),(h); 3,4 | Ordered Fields: [Postscript] [Acrobat] | |
| Chapter 3: Constructing and Writing Proofs | ||||
| September | ||||
| WEEK 3 | 3 - 7 September | |||
| Mon 3 |
LABOR DAY HOLIDAY No class meeting | |||
| Wed 5 | Direct proof | §3.1 #4, 8(a), 9, 15 | Ordered Fields II [Postscript] [Acrobat] | |
| Fri 7 | Proof by contraposition; Biconditionals; Proof by construction. | §3.2 #3,6,18 | Ordered Fields III [Postscript] [Acrobat] | |
| WEEK 4 | 10 - 14 September | |||
| Mon 10 | Proof by contradiction | §3.3 #2,5,21 | Ordered Fields IV: [PostScript] [Acrobat] Do §3.3 #17. | |
| Wed 12 | §3.4 Cases §3.5 Division Algorithm, Congruence | §3.4 #1,2,4,12,13 §3.5 #3,5,11(a),21 | Activity 3.26 p. 125: (Triangle Inequality) Prove 2 as a Lemma; Prove 3. | |
| Chapter 4: Set Theory | ||||
| Fri 14 | §4.1 Operations on Sets | §4.1 #6,10,11,15 | §4.1 #14(a) | |
| WEEK 5 | 6-10 February | |||
| Mon 17 | §4.2 Proving Set Relationships §4.3 Set Algebra | §4.2 #2,4,12,17 §4.3 #3,11 | §4.3 #9 | |
| Wed 19 | §4.4 Cartesian Product | §4.4 #5,6 | §4.4 #9 | |
| Fri 21 | REVIEW of Chapters 1-4, fields, ordered fields | |||
| WEEK 6 | 13-17 February | |||
| Mon 24 | MIDTERM EXAM I Objectives for Exam I. Exam Solutions: [PostScript] [Acrobat] | |||
| Chapter 6: Functions | ||||
| Wed 26 | §§6.1-2 Functions Ordered Pair Representation pp. 319-320. | §6.1 #3,6(a)-(e),(g) §6.2 #1,4 | No homework assignment. | |
| Fri 28 | §6.3 Injective, surjective, bijective functions §6.4 Composition of functions | §6.3 #1-4 §6.4 #4,8 | §6.4 #6(b) | |
| October | ||||
| Limit and Derivative | ||||
| WEEK 7 | 1 - 5 October | |||
| Mon 1 | Limit: definition, uniqueness, linearity. | Limits I: [PostScript] [Acrobat] | ||
| Wed 3 | Limit of a product. | Limit of a product: [PostScript] [Acrobat] | ||
| Fri 5 | Limit of a quotient. | Limit of a quotient: [PostScript] [Acrobat] | ||
| WEEK 8 | 8 - 12 October | |||
| Mon 8 | The Derivative. Linearity. Read §§ 1-7, 9, 13-16, 21, 35 of The Analyst by George Berkeley. Cite three refutations of differential calculus. | The Derivative: [PostScript] [Acrobat] | ||
| Wed 10 | Lagrange's Theorem. | Lagrange's Theorem: [PostScript] [Acrobat] | ||
| Fri 12 | Product and Quotient Rules for Derivatives | Product & Quotient Rules: [PostScript] [Acrobat] | ||
| WEEK 9 | 15-19 October | |||
| Mon 15 | Chain Rule for Derivatives Uphill at a Point Lemma | Chain Rule, Uphill at a Point Lemma [PostScript] [Acrobat] | ||
| Wed 17 | First derivative necessary condition for an extremum; Upper bound and least upper bound. | Extremum, Supremum: [PostScript] [Acrobat] | ||
| Fri 19 | Completeness of the Real Number System | Completeness: [PostScript] [Acrobat] | ||
| WEEK 10 | 22-26 October | |||
| Mon 22 | Intermediate Value Theorem for continuous functions | Review §2.4 #5, Lemma 221.2. | Intermediate Value Theorem [PostScript] [Acrobat] | |
| Wed 24 | Mean Value Theorem Reference (Accessible from ISU computers) | Review §3.3 Proof by Contradiction | Mean Value Theorem [PostScript] [Acrobat] | |
| Fri 26 | First and second derivative tests | 1st & 2nd Derivative tests [PostScript] [Acrobat] | ||
| WEEK 11 | 29 October - 2 November | |||
| Mon 29 | MIDTERM EXAM II Objectives for Exam II. Exam Solutions: [PostScript] [Acrobat] | |||
| Chapter 5: Mathematical Induction | ||||
| Wed 31 | §5.1 Mathematical Induction | §5.1 #3(a),8(b),19 | §5.1 #17(b) | |
| November | ||||
| Fri 2 | §5.2 Mathematical Induction in other forms | §5.2 #2,4,11,18 | Binomial Coefficients: [PostScript] [Acrobat] | |
| WEEK 12 | 5 - 9 November | |||
| Mon 5 | §5.3 Induction and Recursion | §5.3 #2-4,,5(d),9,14 | §5.3 #5(b) | |
| Wed 7 | The Archimedean property | Archimedean property: [PostScript] [Acrobat] | ||
| The Integral | ||||
| Fri 9 | Bounded functions, partitions, Upper and lower sums, definition of integral. | The Integral: [PostScript] [Acrobat] | ||
| WEEK 13 | 12-16 November | |||
| Mon 12 | Integrability Criterion | Integrability [PostScript] [Acrobat] | ||
| Wed 14 | Monotone functions are integrable | Monotone functions integrable [PostScript] [Acrobat] | ||
| Fri 16 | Lipschitz functions. | Lipschitz functions [PostScript] [Acrobat] | ||
| WEEK 14 | 26-30 November | |||
| Mon 26 | Lipschitz functions are integrable. | Lipschitz functions integrable [PostScript] [Acrobat] | ||
| Wed 28 | Linearity of the integral | Linearity [PostScript] [Acrobat] | ||
| Fri 30 | Density of rational and irrational numbers | §3.2 #8 | Rational/irrational [PostScript] [Acrobat] | |
| December | ||||
| WEEK 15 | 3 - 7 December | |||
| Mon 3 | Dirichlet's everywhere-discontinuous, non-integrable function | Non-integrable function: [PostScript] [Acrobat] | ||
| Wed 5 | Mathematical induction: Review of definitions and theorems | Activity 5.13 | ||
| Fri 7 | The integral: Review of definitions and theorems | |||
| FINAL EXAM WEEK | 10-14 December | |||
| Wed 12 | FINAL EXAM 7:30 a.m. - 9:30 a.m. Objectives for Final Exam
| | ||
