Fall 2015 MATH 1131
Introductory Mathematics 數學導論
Syllabus
Announcements
- 2015/9/18 星期五 8:10-8:50 上課教室更動至水利系館4671，僅此一次!!
- 2015/9/18 下星期(第二週)開始將進行拆班，細節確定後會詳細說明。
Class Logs 教學日誌
9/16/2014(WED): Syllabus Introduction and basic outlines.
9/18/2015(FRI): Truth table and negation vs. Sets and complements.
9/23/2015(WED): Disjunction (union) / conjunction (intersection); implication (subset).
9/25/2015(FRI): Subset and powerset.
9/30/2015(WED): More set and statement operations.
10/2/2015(FRI): Quantified statements and paradox.
10/7/2015(WED): Paradox and axiomatic set theory, introduction to direct proofs.
10/9/2015(FRI): 國慶日.
10/14/2015(WED): More examples on direct proofs.
10/16/2015(FRI): Direct proofs on R and sets.
10/21/2015(WED): Disprove and proof by contradiction, existence proofs.
10/23/2015(FRI): Introduction to the natural numbers.
10/28/2015(WED): Examples of induction and well ordering principle.
10/30/2015(FRI): Midterm 1.
11/4/2015(WED): Finish mathematical induction, well-ordered principles.
11/6/2015(FRI): Relations and equivalence relations.
11/11/2015(WED): No class (university anniversary).
11/13/2015(FRI): Equivalence classes.
11/18/2015(WED): Integer modulo n, addition/multiplication on equivalence classes.
11/20/2015(FRI): Introduction to functions.
11/25/2015(WED): Injective/surjective/bijective functions, functions on equivalence classes.
11/27/2015(FRI): Finish discussions on functions.
12/2/2015(WED): Introduction to cardinalities, countable sets.
12/4/2015(FRI): More properties of countable sets.
12/9/2015(WED): Uncountable sets, comparison of cardinalities.
12/11/2015(FRI): Schroder-Bernstein Theorem.
12/16/2015(WED): Finish Schroder-Bernstein Theorem.
12/18/2015(FRI): Midterm 2.
12/23/2015(WED): Elementary measure theory.
Homework Assignments
除非另外聲明，以下題目皆為課本習題。
- Homework 1 (Due Wednesday, September 23)
Chapter 1 (p29~): 2, 5, 36, 39, 42, 78.
Chapter 2 (p64~): 2, 4, 7, 14, 17.
- Homework 2 (Due Wednesday, September 30)
Chapter 1 (p29~): 12, 15, 20, 25, 36, 39, 42, 43, 45, 78.
Chapter 2 (p64~): 2, 4, 7, 14, 16, 17, 20, 25, 49, 91.
Solutions
Grading Criteria
- Homework 3 (Due Wednesday, October 7)
Chapter 1 (p29~): 13, 24, 26, 29, 32, 47, 51, 56, 64, 66, 85.
Chapter 2 (p64~): 31, 35, 62, 68, 71.
Solutions
Grading Criteria
- Homework 4 (Due Wednesday, October 14)
Chapter 3 (p93~): 4, 7, 11, 14, 18, 24, 51, 56, 65.
Solutions
Grading Criteria
- Homework 5 (Due Wednesday, October 21)
Chapter 3 (p93~): 31, 35.
Chapter 4 (p114~): 4, 10, 13, 16, 24, 30, 31, 33, 45, 48, 57, 61, 68, 70.
Solutions
- Homework 6 (Due Wednesday, October 28)
Chapter 5 (p137~): 3, 9, 14, 18, 24, 32, 40, 41, 44, 51, 61.
Chapter 6 (p165~): 4, 9, 13, 16.
Solutions
- Homework 7 (Due Wednesday, November 4)
Chapter 6 (p 165~): 25, 31, 34, 40, 41, 45, 57, 61.
- Homework 8 (Due Wednesday, November 18)
Chapter 6 (p165~): 25, 31, 34, 40, 41, 45, 57, 61.
Chapter 8 (p210~): 5, 11, 14, 19, 22, 26, 28, 30, 35, 37, 40 ,42 ,68, 75.
Solutions
Refined proofs for some problems
- Homework 9 (Due Wednesday, November 25)
1. Prove Bezout's Identity: For all integers a,b, (a,b)=d <==> There exist integers x, y so that ax+by=d.
Chapter 8 (p210~): 57, 59, 77, 81.
Chapter 9 (p234~): 6, 10, 11, 12, 16.
Solutions
- Homework 10 (Due Wednesday, December 2)
Chapter 9 (p234~): 23, 26, 29, 32, 41, 45, 48, 52, 53, 57, 81.
and supplementary problems.
Solutions
- Homework 11 (Due Wednesday, December 9)
Chapter 10 (p262~): 1, 4, 5, 13, 15, 18, 40, 41.
and supplementary problems.
Solutions
- Homework 12 (Due Wednesday December 16)
Chapter 10 (p262~): 20, 21, 24, 27, 32, 34, 42, 49.
and supplementary problems.
Solutions
- Homework 13 (Due Wednesday December 20)
Download Here.
Exams
Lecture Notes