Discrete Structures

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Instructor: Dr. Shieu-Hong Lin

Class Time: **T
TH **at **Lim 041**

· Contact Dr. Lin in advance to set up an appointment by email.

· M T Th 9:00-10:30am 1:30-3:00pm.

Course Syllabus: compact version

**About the reading reports:**

· **Effort (2
points):** How much time have you spent for the reading?
What percentage of the contents in the reading do you think you understand?
Have you come to the class this week? **Assessment**: The student is
expected to **(i)** have attended the class this week at least
once (0.5 point), and**(ii) have either **gained a good understanding
of **80% or more of the contents** **or** have spent at
least **three hours** in the reading (1.5 points).

· **Reflection on
the reading (2 points)**: Put down 1~2 paragraphs of your thoughts such as notes of new
insight you gained, interesting things encountered, questions of things you
don’t understand, and so forth.** ****Assessment**: the student is
expected to show substantial evidence of understanding or effort of trying to
understand the contents in the reading.

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**Week 1: Introduction
to Propositional Logic**

- Reading
#1, due Tuesday,
**Jan. 16****:**(i) Carefully read Sections 1.1 and 1.3 in Discrete*Mathematics and Its Applications*, 7th Ed. Submit your report online under Canvas. (ii) Read Section 1.2 if it takes**less than****3 hours**for you to read 1.1 and 1.3 in (i). **Homework #1,**Tuesday,**Jan. 16****: Please click here**to download**propositional logic.**Either**hand in your work on paper**in the class or**scan and upload an electronic version**under Canvas.**Clarification on Homework #1****:**(i) For problem #1 and #3, your compound proposition should only be composed of the three atomic propositions D4, D100 and D400, parentheses as needed, and the logic operators ˄, ˅, and ̚ as needed. Don’t use other logic operators. (ii) For problem #5, please do include 8 rows in the truth table, corresponding to all the 8 possible combinations of truth values for three independent atomic propositions. Do so even though the truth values D4, D100 and D400 are dependent and some of the 8 combinations could not happen.

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**Week ****2:
Algebraic Laws and Logical Equivalence in Propositional Logic**

- Reading #2, due Tuesday,
**Jan. 23****:**(i) Review Sections 1.1 and 1.3 in Discrete*Mathematics and Its Applications*, 7th Ed. again. (ii) Read Section 1.2 and Section 1.4. **Homework #2,**due Tuesday,**Jan. 23****: Please click here**to download**propositional logic**.

Showcase: An Eclipse logic program for solving Sudoku puzzles

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**Week ****3:
Introduction to Predicate Logic. **

- Reading #3, due Tuesday,
**Jan. 30****:**Read Sections 1.4 and 1.5 in Discrete*Mathematics and Its Applications*, 7th Ed. **Homework #3**, due Tuesday**Jan. 30**, extended to**Feb. 6****: Please click here**to download**predicate logic**.

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**Week ****4:
Predicate Logic, Rules of Inference, and Basics of Proofs****.
**

- Reading #4, due Tuesday,
**Feb. 6****:**(i) Review Sections 1.4 and 1.5 in Discrete*Mathematics and Its Applications*, 7th Ed. if you need more exposure to familiar with predicate logic. (ii) Read Sections 1.6-1.8 if you are confident about Sections 1.4 and 1.5.

** **** **

**Week ****5:
Review on Logic + Basics of Sets. **

- Reading #5, due Tuesday,
**Feb. 13****:**(i) Read Sections 1.6-1.8. (ii) Review Sections 1,1, 1.3, 1.4 and 1.5 in Discrete*Mathematics and Its Applications*, 7th Ed.to prepare for Test #1. (iii) Optional: Read Sections 2.1-2.2 if you have time.

** **** **

**Week 6: Sets, Set Operations,
and Proofs **

- Reading
#6, due Thursday,
**Feb. 22****:****Review**Sections 1.6-1.8 and**Sections 2.1-2.2**in Discrete*Mathematics and Its Applications*, 7th Ed. **Homework #4**due Thursday,**Feb. 22****: Please click here**to download**sets and direct proofs.**

**Test #1** on Logic, Thursday, **Feb. 22****: **

**In-class open-book test**: on the subjects in Reading #1 to Reading #5 on logic.- Make sure you understand
the
**all the homework problems and the related**concepts very well. - Make sure you understand
the
**algebraic laws and logic equivalence**depicted in**Tables 6, 7, and 8**in Section 1.3 and are capable of using them for determining logic equivalence.

** **** **

**Week 7: ****More
on Sets, Set
Operations, and Proofs | ****Basics of
Counting **

- Reading
#7, due Thursday,
**March. 8****:****Read**Sections 6.1, 6.3 and 8.5 in Discrete*Mathematics and Its Applications*, 7th Ed. **Homework #5**due Thursday,**March. 8****: Please click here**to download**sets and direct proofs.**

** **** **

**Weeks 8 and 9: Basics of
Counting **

- Reading
#8 + #9 due
Thursday,
**March. 22****:**Read**Sections 6.1~6.4**and**8.5**(note that 6.2 & 6.4 are new) in Discrete*Mathematics and Its Applications*, 7th Ed. - Homework
#6
**: Please click here**Homework #6 on**counting and derangement,**due Thursday,**March. 22**. - Homework
#7
**: Please click here**Homework #7 on**counting,**due Thursday,**March. 29**.

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**TAs: **Liam Thompson,** **Peter Young**. **

**TA
hours in MATH lab (Lim 143): **Wednesday Liam Thompson: **10:30-11:30am****;** Peter Young: **3:00-4:00pm**

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