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Textbook:	Introduction to Real Analysis, 4th ed., by Bartle and Sherbert.

HW set	section pages	note to yourself of due date	Homework Instructions⊕     and     Handouts⊕
			ER 0.0.1. Read the Homework Instructions and list at least 5 items you want to remember. ER 0.0.2. Read the Writing Guidelines (WG) on the Handout page. List at least 5 items to remember.

HW is posted on Blackboard. The below list is not current. Please see Bb for current list.

Since induction (§1.2) is covered in Math 300, there will be no formal lectures over §1.2.
Here is a summary and 3 examples of proofs by induction to help with §1.2.

• ER 0.0.1. Read the Homework Instructions and list at least 5 items you want to remember.
• ER 0.0.2. Read the Writing Guidelines (WG) on the Handout page. List at least 5 items to remember.
• ER 1.2.5
• ER 1.2.14   (Use induction. Do not use calculus.)
• ER 1.2.15   (Use induction. Do not use calculus.)
• ER 1.2.20
• ER 1.1.1
• ER 1.1.4 Variant. Show Thm 1.1.4⁺ part (2), which is a DeMorgan Law. You may use symbolic logic language, as we did in class for part (1).
• ER 1.1.5.
• ER 1.1.7
• ER 1.1.10
• ER 1.1.19a. You may use (3) and (4) from Functions and Sets.
• ER 1.1.19b. You may use (3) and (4) from Functions and Sets.
• ER 1.1.15 Variant. Verify (8) from Functions and Sets, which is about preimages of unions. You may use symbolic logic language, as we did in class for (9).
• ER 1.1.21. You may use the result shown in class that if f and g are injective then g ∘ f is injective.
• ER 1.1.23
• ER 2.1.17. Will use this ER and Thm 2.1.9 lots.
• ER 2.1.18
• ER 2.1.22 (a) and (b). For (a), do by using Bernoulli's inequality (Ex. 2.1.13).
• ER 2.1.51 Not in book. An application of the Geometric-Arithmetic Mean inequality (see book's Example 2.1.13).
• ER 2.2.51 Not in book. The 4 triangle inequalities.
• ER 2.2.18a Variant max/min via midpt
• ER 2.2.16 Variant ε-NBHDs: ∩ and ∪
• ER 2.2.17 Variant making disjoint ε-NBHDs
• ER 2.3.5 Variant max/min and sup/inf chart
• ER 2.3.10 Variant sup of a union
• ER 2.3.11 Variant sup/inf for A⊆B
• ER 2.4.1 Variant sup for 1-1/n
• ER 2.4.2 Variant sup and inf for 1/j - 1/k
• ER 2.4.4a Variant inf when multiply a set by postive number
• ER 2.4.4b Variant sup/inf when multiply a set by negative number
• ER 2.4.8 Variant sup of the range of sum of 2 function
• ER 2.4.14 Variant dyadics
• ER 2.4.19 Variant density
• ER 2.5.7+2.5.8 Variant NIP closed
• ER 2.5.9 Variant NIP bounded
• ER 2.5.10 Variant NIP [a,b]
• ER 3.1.5c
• ER 3.1.12
• ER 3.1.18
• ER 1.3.6
• ER 1.3.8
• ER 1.3.13. Can use, without proving, ER 1.3.12, which says: card of power set of a set with n elements is 2ⁿ.   [the collection ℱ(ℕ) of finite subets of ℕ is countable]
• ER 1.3.51   [card of finite-vs-infinite sequences of 0's and 1's]
• ER 3.2.51 ERs 3.2.51-3.2.53 go together. Read all three before attempting any of them.
• ER 3.2.52 ERs 3.2.51-3.2.53 go together. Read all three before attempting any of them.
• ER 3.2.53 ERs 3.2.51-3.2.53 go together. Read all three before attempting any of them.
• ER 3.4.9
• ER 3.4.11
• ER 3.4.17. Hint on ER 3.4.17   If you explain your answer intitutively, then a formal proof is not needed.

HW is posted on Blackboard. This list is not current. Please see Bb for current list.