Math 151 202309 Section A01 Schedule

Date

Time

Lecture Number

Topic

Textbook Sections

Quiz/Test Information

Wed, Sep 6

9:30-10:20

Lecture 1

Basic Set Theory: ​elements, union, ​intersection, complement.

5.1


Fri, Sep 8

9:30-10:20

Lecture 2

The Inclusion-Exclusion ​Principle, Venn Diagrams

5.2


Tue, Sep 12

9:30-10:20

Lecture 3

More Venn Diagrams, ​Multiplication Principle

5.3, 5.4


Wed, Sep 13

9:30-10:20

Lecture 4

Multiplication Principle ​(continued), Permutations ​and Combinations

5.4, 5.5


Fri, Sep 15

9:30-10:20

Lecture 5

Permutations and ​Combinations ​(continued), Further ​Counting Techniques

5.5, 5.6


Tue, Sep 19

9:30-10:20

Lecture 6

Permutations, ​Combinations and ​Counting Techniques ​(continued), The Binomial ​Theorem

5.5, 5.6, 5.7


Tue, Sep 19

11:00 PM


Quiz 1 due. Covers ​everything up to end of ​Section 5.4


Best 8 quizzes are worth ​32%

Tue, Sep 19



Last day to drop courses ​and get a 100% fee refund



Wed, Sep 20

9:30-10:20

Lecture 7

MSAC announcement. ​The Binomial Theorem ​(continued), Sample ​Spaces and Events

5.7, 6.1


Fri, Sep 22

9:30-10:20

Lecture 8

Sample Spaces and ​Events (continued), ​Assignment of ​Probabilities

6.1, 6.2


Fri, Sep 22



Last day to add courses



Tue, Sep 26

9:30-10:20

Lecture 9

Assignment of ​Probabilities (continued), ​Calculating Probabilities

6.2, 6.3


Tue, Sep 26

11:00 PM


Quiz 2 due. Covers ​everything from start of ​Section 5.5 to end of ​Section 6.1


Best 8 quizzes are worth ​32%

Wed, Sep 27

9:30-10:20

Lecture 10

Calculating Probabilities ​(continued), Conditional ​Probability and ​Independence

6.3, 6.4

Test 1 Cutoff (End of ​Section 6.3)

Fri, Sep 29

9:30-10:20

Lecture 11

Conditional Probability ​and Independence ​(continued)

6.4


Tue, Oct 3

9:30-10:20

Lecture 12

Review of ​Ordered/Unordered ​Selection, Conditional ​Probability and ​Independence ​(continued)

6.4


Tue, Oct 3

11:00 PM


Quiz 3 due. Covers ​Sections 6.2 and 6.3


Best 8 quizzes are worth ​32%

Wed, Oct 4

9:30-10:20

Test 1

Test 1 covers everything ​so far up to the end of ​Section 6.3


Worth 21%

Fri, Oct 6

9:30-10:20

Lecture 13

Tree diagrams

6.5


Tue, Oct 10



Last day to drop classes ​and get a 50% refund



Tue, Oct 10

9:30-10:20

Lecture 14

Baye's Theorem

6.6


Tue, Oct 10

11:00 PM


Quiz 4 due. Covers ​Section 6.4


Best 8 quizzes are worth ​32%

Wed, Oct 11

9:30-10:20

Lecture 15

Random Variables and ​Probability Distributions

7.2


Fri, Oct 13

9:30-10:20

Lecture 16

Binomial Trials

7.3


Tue, Oct 17

9:30-10:20

Lecture 17

The Mean

7.4


Tue, Oct 17

11:00 PM


Quiz 5 due. Covers ​Sections 6.5 and 6.6


Best 8 quizzes are worth ​32%

Wed, Oct 18

9:30-10:20

Lecture 18

Systems of Linear ​Equations with Unique ​Solutions

2.1


Fri, Oct 20

9:30-10:20

Lecture 19

Systems of Linear ​Equations with Unique ​Solutions (continued), ​General Systems of ​Linear Equations

2.1, 2.2


Tue, Oct 24

9:30-10:20

Lecture 20

Systems of Linear ​Equations (continued)

2.2

Test 2 Cutoff (End of ​Section 2.2)

Tue, Oct 24

11:00 PM


Quiz 6 due. Covers ​Chapter 7


Best 8 quizzes are worth ​32%

Wed, Oct 25

9:30-10:20

Lecture 21

Arithmetic Operations on ​Matrices

2.3


Fri, Oct 27

9:30-10:20

Lecture 22

Arithmetic Operations on ​Matrices (continued)

2.3


Tue, Oct 31



Last day to withdraw from ​courses without penalty ​of failure



Tue, Oct 31

9:30-10:20

Lecture 23

The Inverse of a Matrix, ​Calculating Inverses

2.4, 2.5


Tue, Oct 31

11:00 PM


Quiz 7 due. Covers ​Sections 2.1 and 2.2


Best 8 quizzes are worth ​32%

Wed, Nov 1

9:30-10:20

Test 2

Test 2 covers from the ​start of Section 6.4 to the ​end of Section 2.2


Worth 21%

Fri, Nov 3

9:30-10:20

Lecture 24

The Inverse of a Matrix, ​Calculating Inverses ​(continued), Linear ​Inequalities

2.4, 2.5, 3.1


Tue, Nov 7

9:30-10:20

Lecture 25

A Linear Programming ​Problem, Fundamental ​Theorem of Linear ​Programming

3.2, 3.3


Tue, Nov 7

11:00 PM


Quiz 8 due. Covers ​Sections 2.3 and 2.4


Best 8 quizzes are worth ​32%

Wed, Nov 8

9:30-10:20

Lecture 26

Fundamental Theorem of ​Linear Programming ​(continued), Linear ​Programming

3.3, 3.4


Fri, Nov 10

9:30-10:20

Lecture 27

Linear Programming

3.4


Tue, Nov 14



Reading break (no ​classes, no quiz)



Wed, Nov 15



Reading break (no ​classes)



Fri, Nov 17

9:30-10:20

Lecture 28

Introduction to Markov ​Chains

Handbook Ch 6


Tue, Nov 21

9:30-10:20

Lecture 29

Introduction to Markov ​Chains (continued)

Handbook Ch 6


Tue, Nov 21

11:00 PM


Quiz 9 due. Covers ​Section 2.5 and Chapter 3 ​up to 3.3


Best 8 quizzes are worth ​32%

Wed, Nov 22

9:30-10:20

Lecture 30

Regular Markov Chains

Handbook Ch 6


Fri, Nov 24

9:30-10:20

Lecture 31

Regular Markov Chains ​(continued)

Handbook Ch 6


Tue, Nov 28

9:30-10:20

Lecture 32

Absorbing Markov Chains

Handbook Ch 6


Tue, Nov 28

11:00 PM


Quiz 10 due. Covers ​Section 3.4 and Intro to ​Markov Chains


Best 8 quizzes are worth ​32%

Wed, Nov 29

9:30-10:20

Lecture 33

Absorbing Markov Chains ​(continued)

Handbook Ch 6

Test 3 Cutoff (End of ​Course)

Fri, Dec 1

9:30-10:20


Currently, no lecture ​scheduled. This may ​change later, if more time ​is needed.



Tue, Dec 12 in McKinnon ​Gym

7:00 PM

Test 3

Test 3 covers from the ​start of Section 2.3 to the ​end of the course. Some ​students who missed one ​of Tests 1 and 2 (with ​proper justification) will ​have the opportunity to ​do a make-up test. See ​the course outline for full ​details on course policies.


Worth 26%

Math 151 202309 Section A02 Schedule

Date

Time

Lecture Number

Topic

Textbook Sections

Quiz/Test Information

Wed, Sep 6

12:30-1:20

Lecture 1

Course Outline ​Discussion. Basic Set ​Theory: elements, union, ​intersection, complement.

5.1


Fri, Sep 8

12:30-1:20

Lecture 2

The Inclusion-Exclusion ​Principle

5.2


Tue, Sep 12

12:30-1:20

Lecture 3

Multiplication Principle

5.3, 5.4


Wed, Sep 13

12:30-1:20

Lecture 4

Multiplication Principle ​(continued), Permutations ​and Combinations

5.4, 5.5


Fri, Sep 15

12:30-1:20

Lecture 5

Permutations and ​Combinations ​(continued), Further ​Counting Techniques

5.5, 5.6


Tue, Sep 19

12:30-1:20

Lecture 6

Permutations, ​Combinations and ​Counting Techniques ​(continued), The Binomial ​Theorem

5.5, 5.6, 5.7


Tue, Sep 19

11:00 PM


Quiz 1 due. Covers ​everything up to end of ​Section 5.4


Best 8 quizzes are worth ​32%

Tue, Sep 19



Last day to drop courses ​and get a 100% fee refund



Wed, Sep 20

12:30-1:20

Lecture 7

MSAC announcement. ​The Binomial Theorem ​(continued), Sample ​Spaces and Events

5.7, 6.1


Fri, Sep 22

12:30-1:20

Lecture 8

Sample Spaces and ​Events (continued), ​Assignment of ​Probabilities

6.1, 6.2


Fri, Sep 22



Last day to add courses



Tue, Sep 26

12:30-1:20

Lecture 9

Assignment of ​Probabilities (continued), ​Calculating Probabilities

6.2, 6.3


Tue, Sep 26

11:00 PM


Quiz 2 due. Covers ​everything from start of ​Section 5.5 to end of ​Section 6.1


Best 8 quizzes are worth ​32%

Wed, Sep 27

12:30-1:20

Lecture 10

Calculating Probabilities ​(continued), Conditional ​Probability and ​Independence

6.3, 6.4

Test 1 Cutoff (End of ​Section 6.3)

Fri, Sep 29

12:30-1:20

Lecture 11

Conditional Probability ​and Independence ​(continued)

6.4


Tue, Oct 3

12:30-1:20

Lecture 12

Review of ​Ordered/Unordered ​Selection, Conditional ​Probability and ​Independence ​(continued)

6.4


Tue, Oct 3

11:00 PM


Quiz 3 due. Covers ​Sections 6.2 and 6.3


Best 8 quizzes are worth ​32%

Wed, Oct 4

12:30-1:20

Test 1

Test 1 covers everything ​so far up to the end of ​Section 6.3


Worth 21%

Fri, Oct 6

12:30-1:20

Lecture 13

Tree diagrams

6.5


Tue, Oct 10



Last day to drop classes ​and get a 50% refund



Tue, Oct 10

12:30-1:20

Lecture 14

Baye's Theorem

6.6


Tue, Oct 10

11:00 PM


Quiz 4 due. Covers ​Section 6.4


Best 8 quizzes are worth ​32%

Wed, Oct 11

12:30-1:20

Lecture 15

Random Variables and ​Probability Distributions

7.2


Fri, Oct 13

12:30-1:20

Lecture 16

Binomial Trials

7.3


Tue, Oct 17

12:30-1:20

Lecture 17

The Mean

7.4


Tue, Oct 17

11:00 PM


Quiz 5 due. Covers ​Sections 6.5 and 6.6


Best 8 quizzes are worth ​32%

Wed, Oct 18

12:30-1:20

Lecture 18

Systems of Linear ​Equations with Unique ​Solutions

2.1


Fri, Oct 20

12:30-1:20

Lecture 19

Systems of Linear ​Equations with Unique ​Solutions (continued), ​General Systems of ​Linear Equations

2.1, 2.2


Tue, Oct 24

12:30-1:20

Lecture 20

Systems of Linear ​Equations (continued)

2.2

Test 2 Cutoff (End of ​Section 2.2)

Tue, Oct 24

11:00 PM


Quiz 6 due. Covers ​Chapter 7


Best 8 quizzes are worth ​32%

Wed, Oct 25

12:30-1:20

Lecture 21

Arithmetic Operations on ​Matrices (continued)

2.3


Fri, Oct 27

12:30-1:20

Lecture 22

Arithmetic Operations on ​Matrices (continued)

2.3


Tue, Oct 31



Last day to withdraw from ​courses without penalty ​of failure



Tue, Oct 31

12:30-1:20

Lecture 23

The Inverse of a Matrix, ​Calculating Inverses

2.4, 2.5


Tue, Oct 31

11:00 PM


Quiz 7 due. Covers ​Sections 2.1 and 2.2


Best 8 quizzes are worth ​32%

Wed, Nov 1

12:30-1:20

Test 2

Test 2 covers from the ​start of Section 6.4 to the ​end of Section 2.2


Worth 21%

Fri, Nov 3

9:30-10:20

Lecture 24

The Inverse of a Matrix, ​Calculating Inverses ​(continued), Linear ​Inequalities

2.4, 2.5, 3.1


Tue, Nov 7

9:30-10:20

Lecture 25

A Linear Programming ​Problem, Fundamental ​Theorem of Linear ​Programming

3.2, 3.3


Tue, Nov 7

11:00 PM


Quiz 8 due. Covers ​Sections 2.3 and 2.4


Best 8 quizzes are worth ​32%

Wed, Nov 8

9:30-10:20

Lecture 26

Fundamental Theorem of ​Linear Programming ​(continued), Linear ​Programming

3.3, 3.4


Fri, Nov 10

9:30-10:20

Lecture 27

Linear Programming

3.4


Tue, Nov 14



Reading break (no ​classes, no quiz)



Wed, Nov 15



Reading break (no ​classes)



Fri, Nov 17

9:30-10:20

Lecture 28

Introduction to Markov ​Chains

Handbook Ch 6


Tue, Nov 21

9:30-10:20

Lecture 29

Introduction to Markov ​Chains (continued)

Handbook Ch 6


Tue, Nov 21

11:00 PM


Quiz 9 due. Covers ​Section 2.5 and Chapter 3 ​up to 3.3


Best 8 quizzes are worth ​32%

Wed, Nov 22

9:30-10:20

Lecture 30

Regular Markov Chains

Handbook Ch 6


Fri, Nov 24

9:30-10:20

Lecture 31

Regular Markov Chains ​(continued)

Handbook Ch 6


Tue, Nov 28

9:30-10:20

Lecture 32

Absorbing Markov Chains

Handbook Ch 6


Tue, Nov 28

11:00 PM


Quiz 10 due. Covers ​Section 3.4 and Intro to ​Markov Chains


Best 8 quizzes are worth ​32%

Wed, Nov 29

9:30-10:20

Lecture 33

Absorbing Markov Chains ​(continued)

Handbook Ch 6

Test 3 Cutoff (End of ​Course)

Fri, Dec 1



Currently, no lecture ​scheduled. This may ​change later, if more time ​is needed.



Tue, Dec 12 in McKinnon ​Gym

7:00 PM

Test 3

Test 3 covers from the ​start of Section 2.3 to the ​end of the course. Some ​students who missed one ​of Tests 1 and 2 (with ​proper justification) will ​have the opportunity to ​do a make-up test. See ​the course outline for full ​details on course policies.


Worth 26%

Math 122 202209 Section A03 Schedule

Date

Time

Lecture Number

Topic

Lecture Notes ​Sections

ICA

Assignment due dates

Wed, Sep 7

9:30-10:20

Lecture 1

Intro to the course. ​Statements, ​compound ​statements, negation.

1.1, 1.2, 1.3



Fri, Sep 9

9:30-10:20

Lecture 2

Truth tables, ​tautologies, ​contradiction

1.4, 1.5

lCA 1, start of class


Tue, Sep 13

9:30-10:20

Lecture 3

Logical equivalence. ​Logical implication. ​Converse and ​contrapositive. ​Necessary and ​sufficient.

1.6, 1.11, 1.7

ICA 2, truth tables


Wed, Sep 14

9:30-10:20

Lecture 4

Laws of logic and ​other Known LEs.

1.9



Fri, Sep 16

9:30-10:20

Lecture 5

Every logical ​statement can be ​expressed with just ​∧, ∨ and ¬. Valid ​arguments and ​inference rules. Proof ​by contradiction.

1.10, 1.12



Tue, Sep 20

9:30-10:20

Lecture 6, Quiz 1

More valid arguments, ​proof by cases. Quiz 1 ​at end of class.

1.12, 1.13



Tue, Sep 20



Last day to drop ​courses and get a ​100% fee refund




Wed, Sep 21

9:30-10:20

Lecture 7

Open statements, ​quantifiers. Negating ​statements involving ​quantifiers.

2.1, 2.2, 2.3

ICA 3 (valid ​arguments and ​counterexamples; ​they will find this ​hard)


Fri, Sep 23

9:30-10:20

Lecture 8

Math & Stats ​Assistance Centre ​Announcement. ​Examples of proofs.

2.4



Fri, Sep 23



Last day to add ​courses




Tue, Sep 27

9:30-10:20

Lecture 9

Examples of proofs, ​continued. ​Introduction to sets.

2.4, 3.1

ICA 4, quantifiers

Assignment 1

Wed, Sep 28

9:30-10:20

Lecture 10

Set membership and ​set equality. The ​empty set, special ​sets. Subsets

3.1, 3.2, 3.4, 3.5, 3.3, ​3.6, 3.7

ICA 5 (a proof)


Fri, Sep 30



National Day for Truth ​and Reconciliation (no ​classes)




Tue, Oct 4

9:30-10:20

Lecture 11, Quiz 2

Set operations, ​complements and the ​laws of set theory. ​Quiz 2 at end of class.

3.10, 3.11



Wed, Oct 5

9:30-10:20

Lecture 12

Proofs involving sets.

3.10, 3.11, 3.8



Fri, Oct 7

9:30-10:20

Lecture 13

The power set. Set ​proofs involving ​subsets.

3.11, 3.1

ICA 6 (Jeopardy, end ​of class)


Tue, Oct 11



Last day to drop ​classes and get a 50% ​refund




Tue, Oct 11

9:30-10:20

Lecture 14

Counting sets and ​subsets. Venn ​diagrams.

3.13, 3.9, 3.12


Assignment 2

Wed, Oct 12

9:30-10:20

Lecture 15

Inclusion-exclusion. ​Inclusion-exclusion ​examples.

3.12, 3.14,

ICA 7 (power set)


Fri, Oct 14

9:30-10:20

Lecture 16

More inclusion-​exclusion examples. ​Introduction to ​Mathematical ​Induction.

3.14, 4.6, 4.7

ICA 8 (Set proof?)


Tue, Oct 18

9:30-10:20

Lecture 17, Quiz 3

Induction and ​recursion examples. ​Quiz 3 at end of class.

4.1, 4.2, 4.3, 4.6, 4.7, ​4.8



Wed, Oct 19

9:30-10:20

Lecture 18

Recursive definitions. ​Strong induction. ​Induction examples ​continued.

4.1, 4.4, 4.7, 4.8

ICA 8, end of class


Fri, Oct 21

9:30-10:20

Lecture 19

Some special sums. ​Solving 1-term ​recurrences.

4.9



Tue, Oct 25

9:30-10:20

Lecture 20

Division algorithm. ​Floors and ceilings. ​Representing ​numbers in base b.

5.1, 5.2, 5.3


Assignment 3

Wed, Oct 26

9:30-10:20

Lecture 21

More changing bases. ​Divisibility. Prime ​numbers. ​Fundamental ​Theorem of ​Arithmetic.

5.5, 5.6, 5.8

ICA 9, changing base


Fri, Oct 28

9:30-10:20

Lecture 22

More FTA, Irrationality ​proofs. Infinitude of ​primes.

5.7, 5.9,



Mon, Oct 31



Last day to withdraw ​from courses without ​penalty of failure




Tue, Nov 1

9:30-10:20

Lecture 23, Quiz 4

More divisibility and ​FTA, gcd, lcm. Quiz 4 ​at end of class.

5.10, 5.11, 5.12



Wed, Nov 2

9:30-10:20

Lecture 24

Euclidean Algorithm ​and Integer linear ​combinations.

5.12, 5.13

ICA 10 Euclidean


Fri, Nov 4

9:30-10:20

Lecture 25

More integer linear ​combinations. ​Relatively Prime. ​Modular arithmetic.

5.14, 5.15



Tue, Nov 8

9:30-10:20

Lecture 26

Cool Modular ​Arithmetic Tricks. ​Divisibility by 3 and 9. ​Cartesian product. ​Maybe a little intro to ​relations.

5.16, 6.1, 6.2, 6.3

ICA 11, ax+by and find ​last digit

Assignment 4

Wed, Nov 9



Reading break (no ​classes)




Fri, Nov 11



Reading break (no ​classes)




Tue, Nov 15

9:30-10:20

Lecture 27

More relations. ​Reflexive, symmetric, ​transitive and ​antisymmetric ​relations.

6.4, 6.5, 6.6, 6.7

ICA 14

Check out UVic's 5 ​Days of Action (Not ​for Course Credit)

Wed, Nov 16

9:30-10:20

Lecture 28

Equivalence relations, ​partitions

6.9, 6.10

ICA 15


Fri, Nov 18

9:30-10:20

Lecture 29, Quiz 5

More about relations ​and partitions. A bit of ​functions. Quiz 5 at ​end of class.

6.9, 6.10, 7.1



Tue, Nov 22

9:30-10:20

Lecture 30

Introduction to ​functions

7.1



Wed, Nov 23

9:30-10:20

Lecture 31

Injectivity, surjectivity ​and bijectivity

7.3, 7.4, 7.5



Fri, Nov 25

9:30-10:20

Lecture 32

Function composition. ​The identity function ​and inverses.

7.6, 7.6, 7.8


Assignment 5

Tue, Nov 29

9:30-10:20

Lecture 33

Introduction to ​cardinality, ​countability

8.1, 8.2, 8.3



Wed, Nov 30

9:30-10:20

Lecture 34

Uncountablility

8.4, 8.5, 8.6



Fri, Dec 2

9:30-10:20

Lecture 35, Quiz 6

More cardinality ​examples. Quiz 6 at ​end of class.

8.7, 8.8



Mon, Dec 5



Currently, no lecture ​scheduled. This may ​change later, if more ​time is needed.




Dec 15

7:00 PM

Final Exam

Worth 40%




Math 122 202209 Section A04 Schedule

Date

Time

Lecture Number

Topic

Lecture Notes ​Sections

ICA

Assignment due dates

Wed, Sep 7

11:30-12:20

Lecture 1

Intro to the course. ​Statements, ​compound ​statements, negation.

1.1, 1.2, 1.3



Fri, Sep 9

11:30-12:20

Lecture 2

Truth tables, ​tautologies, ​contradiction

1.4, 1.5

lCA 1, start of class


Tue, Sep 13

11:30-12:20

Lecture 3

Logical equivalence. ​Logical implication. ​Converse and ​contrapositive. ​Necessary and ​sufficient.

1.6, 1.11, 1.7



Wed, Sep 14

11:30-12:20

Lecture 4

Laws of logic and ​other Known LEs

1.9

ICA 2, start of class ​(converse and ​contrapositive)


Fri, Sep 16

11:30-12:20

Lecture 5

Every logical ​statement can be ​expressed with just ​∧, ∨ and ¬. Valid ​arguments and ​inference rules. Proof ​by contradiction

1.10, 1.12



Tue, Sep 20

11:30-12:20

Lecture 6, Quiz 1

More valid arguments. ​Proof by cases. Quiz 1 ​at end of class.

1.12, 1.13



Tue, Sep 20

11:30-12:20


Last day to drop ​courses and get a ​100% fee refund




Wed, Sep 21

11:30-12:20

Lecture 7

Open statements, ​quantifiers. Negating ​statements involving ​quantifiers.

2.1, 2.2, 2.3

ICA 3 (valid ​arguments and ​counterexamples; ​they will find this ​hard)


Fri, Sep 23

11:30-12:20

Lecture 8

Examples of proofs.

2.4



Fri, Sep 23

11:30-12:20


Last day to add ​courses




Tue, Sep 27

11:30-12:20

Lecture 9

Math & Stats ​Assistance Centre ​Announcement. ​Examples of proofs, ​continued. ​Introduction to sets.

2.4, 3.1

ICA 4 quantifiers

Assignment 1

Wed, Sep 28

11:30-12:20

Lecture 10

Set membership and ​set equality. The ​empty set, special ​sets. Subsets

3.1, 3.2, 3.4, 3.5, 3.3, ​3.6, 3.7

ICA 5 (a proof)


Fri, Sep 30

11:30-12:20


National Day for Truth ​and Reconciliation (no ​classes)




Tue, Oct 4

11:30-12:20

Lecture 11, Quiz 2

Set operations, ​complements and the ​laws of set theory. ​Quiz 2 at end of class.

3.10, 3.11



Wed, Oct 5

11:30-12:20

Lecture 12

Proofs involving sets.

3.10, 3.11, 3.8



Fri, Oct 7

11:30-12:20

Lecture 13

The power set. Set ​proofs involving ​subsets.

3.11, 3.1

ICA 6 (Jeopardy, end ​of class)


Tue, Oct 11

11:30-12:20


Last day to drop ​classes and get a 50% ​refund




Tue, Oct 11

11:30-12:20

Lecture 14

Counting sets and ​subsets. Venn ​diagrams.

3.13, 3.9, 3.12


Assignment 2

Wed, Oct 12

11:30-12:20

Lecture 15

Inclusion-exclusion. ​Inclusion-exclusion ​examples.

3.12, 3.14,

ICA 7 (power set)


Fri, Oct 14

11:30-12:20

Lecture 16

More Inclusion-​Exclusion Examples. ​Introduction to ​Mathematical ​Induction.

3.14, 4.6, 4.7

ICA 8 (Set proof?)


Tue, Oct 18

11:30-12:20

Lecture 17, Quiz 3

Induction and ​recursion examples. ​Quiz 3 at end of class.

4.1, 4.2, 4.3, 4.6, 4.7, ​4.8



Wed, Oct 19

11:30-12:20

Lecture 18

Induction examples ​continued. Recursive ​definitions.

Chapter 4

ICA 9, counting sets


Fri, Oct 21

11:30-12:20

Lecture 19

Some special sums. ​Solving 1-term ​recurrences. Strong ​induction.

Chapter 4



Tue, Oct 25

11:30-12:20

Lecture 20

Division algorithm. ​Floors and ceilings. ​Representing ​numbers in base b.

5.1, 5.2, 5.3

ICA 10, Induction ​proof

Assignment 3

Wed, Oct 26

11:30-12:20

Lecture 21

More changing bases. ​Divisibility. Prime ​numbers. ​Fundamental ​Theorem of ​Arithmetic.

5.5, 5.6, 5.8



Fri, Oct 28

11:30-12:20

Lecture 22

More FTA, Irrationality ​proofs.

5.7, 5.9,

These ICAs are not ​accurate. See ​Crowdmark


Mon, Oct 31

11:30-12:20


Last day to withdraw ​from courses without ​penalty of failure




Tue, Nov 1

11:30-12:20

Lecture 23, Quiz 4

Infinitude of primes. ​gcd, lcm. Quiz 4 at ​end of class.

5.10, 5.11, 5.12



Wed, Nov 2

11:30-12:20

Lecture 24

Euclidean Algorithm ​and Integer linear ​combinations.

5.12, 5.13



Fri, Nov 4

11:30-12:20

Lecture 25

More integer linear ​combinations. ​Relatively Prime. ​Modular arithmetic.

5.14, 5.15



Tue, Nov 8

11:30-12:20

Lecture 26

Cool Modular ​Arithmetic Tricks. ​Divisibility by 3 and 9. ​Cartesian product. ​Maybe a little intro to ​relations.

5.16, 6.1, 6.2, 6.3


Assignment 4

Wed, Nov 9

11:30-12:20


Reading break (no ​classes)




Fri, Nov 11

11:30-12:20


Reading break (no ​classes)




Tue, Nov 15

11:30-12:20

Lecture 27

More relations. ​Reflexive, symmetric, ​transitive and ​antisymmetric ​relations.

6.4, 6.5, 6.6, 6.7


Check out UVic's 5 ​Days of Action (Not ​for Course Credit)

Wed, Nov 16

11:30-12:20

Lecture 28

Equivalence relations, ​partitions

6.9, 6.10



Fri, Nov 18

11:30-12:20

Lecture 29, Quiz 5

More about relations ​and partitions. A bit of ​functions. Quiz 5 at ​end of class.

6.9, 6.10, 7.1



Tue, Nov 22

11:30-12:20

Lecture 30

Introduction to ​functions

7.1



Wed, Nov 23

11:30-12:20

Lecture 31

Injectivity, surjectivity ​and bijectivity

7.3, 7.4, 7.5



Fri, Nov 25

11:30-12:20

Lecture 32

Function composition. ​The identity function ​and inverses.

7.6, 7.6, 7.8


Assignment 5

Tue, Nov 29

11:30-12:20

Lecture 33

Introduction to ​cardinality, ​countability

8.1, 8.2, 8.3



Wed, Nov 30

11:30-12:20

Lecture 34

Uncountablility

8.4, 8.5, 8.6



Fri, Dec 2

11:30-12:20

Lecture 35, Quiz 6

More cardinality ​examples. Quiz 6 at ​end of class.

8.7, 8.8



Mon, Dec 5



Currently, no lecture ​scheduled. This may ​change later, if more ​time is needed.




Dec 15

7:00 PM

Final Exam

Worth 40%




Math 492/529 202209 Schedule

Date

Time

Lecture Number

Topic

Corresponding ​Assignment

Assessment Release ​or Due Dates

Further reading ​"beyond" the topics of ​the lecture (not part ​of the course)

Thu, Sep 8

10:00-11:20

Lecture 1

Course Intro, Section ​2.1: Intersecting ​Families, Section 2.2: ​The Sunflower Lemma

1

All assignments ​released, Optional ​bonus problems ​released, project ​details released

https://arxiv.org/pdf/2​011.14252.pdf ​https://arxiv.org/pdf/1​908.08483.pdf

Mon, Sep 12

10:00-11:20

Lecture 2

Section 2.3: VC ​Dimension, maybe ​asymptotic notation ​and basic probability

1



Thu, Sep 15

10:00-11:20

Lecture 3

Section 1.5 Harris--​Kleitman Inequality, ​Jensen's Inequality

1/2



Mon, Sep 19



Day of Mourning for ​Queen Elizabeth II (no ​classes)




Tue, Sep 20



Last day to withdraw ​and get a 100% fee ​refund




Thu, Sep 22

10:00-11:20

Lecture 4

Section 1.1: Sperner's ​Theorem, Section 1.3: ​The LYM and Local ​LYM Inequalities

2



Fri, Sep 23



Last day to add ​courses




Mon, Sep 26

10:00-11:20

Lecture 5

Section 1.4: The ​Kruskal--Katona ​Theorem

2

Assignment 1 due

https://youtu.be/r6wb​HWMaMAY

Thu, Sep 29

10:00-11:20

Lecture 6

Section 1.4 continued

2



Mon, Oct 3

10:00-11:20

Lecture 7

Section 1.2: The ​Littlewood--Offord ​Problem

2



Thu, Oct 6

10:00-11:20

Lecture 8

Section 3.1: The ​Extremal Number of a ​Triangle, Section 3.2: ​The Extremal Number ​of General Cliques

3



Mon, Oct 10



Thanksgiving (no ​classes)




Tue, Oct 11



Last day to withdraw ​and get a 50% fee ​refund




Tue, Oct 11





Assignment 2 due


Thu, Oct 13

10:00-11:20

Lecture 9

Section 3.3: Turan ​Density of General ​Graphs

3



Mon, Oct 17

10:00-11:20

Lecture 10

Maybe a bit more ​Erdos--Stone. Section ​3.4: Extremal ​Numbers of Bipartite ​Graphs, Section 3.5: ​Better Bounds for ​Even Cycles

3



Thu, Oct 20

10:00-11:20

Lecture 11

More stuff on even ​cycles. Section 4.3: ​Supersaturation for ​Triangles, Section 4.4: ​Supersaturation for ​Quadrangles

4



Mon, Oct 24

10:00-11:20

Lecture 12

Section 4.5: ​Supersaturation for ​Even Cycles

4



Tue, Oct 25





Assignment 3 due


Thu, Oct 27

10:00-11:20

Lecture 13

Section 4.2: ​Approximate ​Supersaturation for ​General Graphs. ​Section 4.1: Stability ​for Turan's Theorem

4



Mon, Oct 31



Last day to withdraw ​without penalty of ​failure




Mon, Oct 31

10:00-11:20

Lecture 14

Section 5.1: Regular ​Pairs and Counting. ​Statements of the ​Regularity and ​Triangle Removal ​Lemmas.

5



Thu, Nov 3

10:00-11:20

Lecture 15

Section 5.2: The ​Regularity and ​Triangle Removal ​Lemmas

5



Mon, Nov 7

10:00-11:20

Lecture 16

Section 5.3: Proof of ​the Regularity Lemma

5



Tue, Nov 8





Assignment 4 due


Thu, Nov 10



Reading break (no ​classes)




Mon, Nov 14

10:00-11:20

Lecture 17

Section 5.3 continued, ​Building up some ​entropy intuition

5

Check out UVic's 5 ​Days of Action (Not ​for Course Credit)


Thu, Nov 17

10:00-11:20

Lecture 18

Section 6.3: Entropy, ​Shearer's Lemma and ​the Loomis--Whitney ​Inequality.

6



Mon, Nov 21

10:00-11:20

Lecture 19

Section 6.4: Counting ​Perfect Matchings. ​Bregman's Theorem. ​Kahn-Lovasz ​Theorem.

6



Tue, Nov 22





Assignment 5 due


Thu, Nov 24

10:00-11:20

Lecture 20

Section 6.5: ​Homomorphism ​densities of trees.

6



Mon, Nov 28

10:00-11:20

Lecture 21

Section 6.2: Counting ​Independent Sets in ​Regular Graphs

6



Thu, Dec 1

10:00-11:20

Lecture 22

Section 6.1: ​Independent Sets in ​Triangle-Free Graphs

6



Tue, Dec 6



Exam period


Assignment 6 due


Mon, Dec 12



Exam period


Projects due, Optional ​bonus problems due


Wed, Dec 14

9:00-12:00

Final exam

Final exam in DTB ​A102


Final exam


Math 122 202109 Section A01 Schedule

Date

Time

Lecture Number

Topic

Lecture Notes ​Sections

ICA

Worksheets due

Thu, Sep 9

8:30-9:50

Lecture 1

Intro to the course. ​Statements, ​compound ​statements, negation. ​Truth tables. ​Tautologies and ​contradictions

1.1, 1.2, 1.3, 1.4, 1.5



Mon, Sep 13

8:30-9:50

Lecture 2

Logical equivalence, ​logical implication. ​Converse and ​contrapositive. ​Necessary and ​sufficient.

1.6, 1.11, 1.7, 1.8

ICA 1, between ​implication and ​converse


Thu, Sep 16

8:30-9:50

Lecture 3

Math Assistance ​Centre ​announcement. Laws ​of logic, everything is ​just ∧, ∨ and ¬, valid ​arguments and ​inference rules

1.9, 1.10, 1.12



Mon, Sep 20

8:30-9:50

Lecture 4

Valid arguments and ​inference rules ​continued. Proofs by ​contradiction and ​cases. Open ​statements, ​introduction to ​quantifiers. Negating ​statements involving ​quantifiers.

1.12, 1.13, 2.1, 2.2, 2.3

ICA 2


Tue, Sep 21



Last day to drop ​courses and get a ​100% fee refund




Wed, Sep 22






Worksheet 1

Thu, Sep 23

8:30-9:50

Lecture 5

Review of valid and ​invalid arguments. ​Quantifiers and their ​negations, continued. ​Examples of proofs

2.2, 2.3, 2.4

ICA 3


Fri, Sep 24



Last day to add ​courses




Mon, Sep 27

8:30-9:50

Lecture 6

Examples of Proofs ​continued. ​Introduction to sets, ​set membership. The ​empty set, special ​sets. Set equality.

2.4, 3.1, 3.2, 3.4, 3.5, ​3.3

Tell them to play with ​LaTeX. Can use ​Crowdmark text ​boxes. Can use ​overleaf.


Wed, Sep 29






Worksheet 2

Thu, Sep 30



National Day for Truth ​and Reconciliation (No ​Classes)




Mon, Oct 4

8:30-9:50

Lecture 7

Subsets and proper ​subsets, set ​operations, ​complements. Laws of ​set theory. Perhaps ​some proofs involving ​sets.

3.4, 3.6, 3.7, 3.10, 3.11

ICA 4, very easy set ​theory. Get them to ​use LaTeX on ​Crowdmark. End of ​lecture.


Wed, Oct 6






Worksheet 3

Thu, Oct 7

8:30-9:50

Lecture 8

Various proofs ​involving sets. The ​power set. Counting ​sets and subsets. ​Venn diagrams.

3.10, 3.11, 3.8. 3.13, ​3.9

ICA 5 (Jeopardy, start ​of class)


Mon, Oct 11

8:30-9:50


Thanksgiving (No ​Classes)




Tue, Oct 12



Last day to drop ​classes and get a 50% ​refund




Wed, Oct 13






Worksheet 4

Thu, Oct 14

8:30-9:50

Lecture 9

A proof using the laws ​of set theory. More ​Venn diagrams. ​Inclusion-exclusion. ​Russel's Paradox.

3.12, 3.14



Mon, Oct 18

8:30-9:50

Lecture 10

Introduction to ​Induction. Weak vs ​strong induction.

4.1, 4.2, 4.3, 4.4

ICA 6


Thu, Oct 21

8:30-9:50

Lecture 10.5

More Induction ​Examples. Term Test ​1 (worth 6.5%)

4.5



Mon, Oct 25

8:30-9:50

Lecture 11

More Induction ​Examples. Some ​special sums. Solving ​recurrence relations.

4.5, 4.6, 4.7, 4.8

ICA 7 (induction ​practice)

No worksheet this ​week

Wed, Oct 27






Worksheet 5

Thu, Oct 28

8:30-9:50

Lecture 12

Division algorithm. ​Floors and ceilings. ​Representing ​numbers in base b.

4.7, 4.9, 5.1, 5.2, 5.3, ​5.4, 5.5

ICA 8 (more ​induction)


Sun, Oct 31



Last day to withdraw ​from courses without ​penalty of failure




Mon, Nov 1

8:30-9:50

Lecture 13

Divisibility. Prime ​numbers. ​Fundamental ​Theorem of ​Arithmetic. Infinitude ​of primes. Irrationality ​proofs.

5.6, 5.7, 5.8, 5.10, 5.11



Wed, Nov 3






Worksheet 6

Thu, Nov 4

8:30-9:50

Lecture 14

Irrationality proofs, ​continued. gcd and ​lcm, Euclidean ​Algorithm

5.8, 5.9, 5.12



Mon, Nov 8

8:30-9:50

Lecture 15

Euclidean Algorithm ​continued. Integer ​linear combinations. ​Relatively prime. ​Modular arithmetic

5.13, 5.14, 5.15

ICA 9 (Euclidean Algo)


Wed, Nov 10



Reading Break (No ​Classes)



No worksheet

Thu, Nov 11



Reading Break (No ​Classes)




Mon, Nov 15

8:30-9:50

Lecture 16

Modular arithmetic, ​continued. Divisibility ​by 3 and 9. Cartesian ​product. Relations. ​Reflexive, symmetric, ​transitive and ​antisymmetric ​relations

5.15, 5.16, 6.1, 6.2, ​6.4, 6.5, 6.6, 6.7

ICA 10 (ax+by and ​modular)


Wed, Nov 17






Worksheet 7

Thu, Nov 18

8:30-9:50

Lecture 17

Reflexive, symmetric, ​transitive and ​antisymmetric ​relations continued. ​Equivalence relations, ​partitions.

6.4, 6.5, 6.6, 6.7

ICA 11


Mon, Nov 22

8:30-9:50

Lecture 18

Equivalence relations, ​partitions, continued. ​Functions. Injectivity, ​surjectivity and ​bijectivity. (Pre-​recorded, click link for ​YouTube stream)

6.9, 6.10, 7.1, 7.3, 7.4, ​7.5



Thu, Nov 25

8:30-9:50

Lecture 18.5

Injectivity, surjectivity ​and bijectivity ​continued (Pre-​recorded, same link ​as last time). Term ​Test 2

7.3, 7.4, 7.5



Mon, Nov 29

8:30-9:50

Lecture 19

Function composition. ​The identity function ​and inverses.

7.6, 7.8

ICA 12


Thu, Dec 2

8:30-9:50

Lecture 20

Introduction to ​cardinality and ​countability. Proving ​countability

8.3, 8.4, 8.5, 8.6

ICA 13


Fri, Dec 3

8:30-9:50





Worksheet 8

Mon, Dec 6

8:30-9:50

Lecture 21

Uncountable sets

8.7, 8.8

ICA 14


Dec 15

7:00 PM

Final Exam

Worth 29%




Math 122 202109 Section A01 Schedule

Date

Time

Lecture Number

Topic

Lecture Notes ​Sections

ICA

Worksheet due dates

Wed, Sep 8

8:30-9:20

Lecture 1

Intro to the course. ​Statements, ​compound ​statements, negation.

1.1, 1.2, 1.3



Fri, Sep 10

8:30-9:20

Lecture 2

Truth tables, ​tautologies, ​contradiction

1.4, 1.5

lCA 1, start of class


Tue, Sep 14

8:30-9:20

Lecture 3

Logical equivalence. ​Logical implication. ​Converse and ​contrapositive.

1.6, 1.11, 1.7



Wed, Sep 15

8:30-9:20

Lecture 4

Math Assistance ​Centre ​announcement. Laws ​of logic, everything is ​just ∧, ∨ and ¬.

1.9, 1.10

ICA 2, start of class, ​after announcement ​(converse and ​contrapositive)


Fri, Sep 17

8:30-9:20

Lecture 5

Necessary and ​sufficient. Reminder: ​contrapositive is only ​for implication. Valid ​arguments and ​inference rules.

1.8, 1.12



Tue, Sep 21

8:30-9:20

Lecture 6

Proof by ​contradiction, proof ​by cases. Open ​statements, ​quantifiers.

1.12, 1.13, 2.1, 2.2

ICA 3 (valid ​arguments and ​counterexamples)


Tue, Sep 21



Last day to drop ​courses and get a ​100% fee refund




Wed, Sep 22

8:30-9:20

Lecture 7

Quantifiers, ​continued. Negating ​statements involving ​quantifiers. Examples ​of proofs.

2.2, 2.3, 2.4


Worksheet 1

Fri, Sep 24

8:30-9:20

Lecture 8

Might need to do ​some review of valid ​arguments. Examples ​of proofs.

1.12, 2.4

ICA 4, end of class


Fri, Sep 24



Last day to add ​courses




Tue, Sep 28

8:30-9:20

Lecture 9

Examples of proofs, ​continued. ​Introduction to sets.

2.4, 3.1

Tell them to start ​playing with LaTeX. ​Can use overleaf or ​Crowdmark.


Wed, Sep 29

8:30-9:20

Lecture 10

Set membership and ​set equality. The ​empty set, special ​sets. Subsets

3.1, 3.2, 3.4, 3.5, 3.3, ​3.6, 3.7


Worksheet 2

Fri, Oct 1

8:30-9:20

Lecture 11

Set operations, ​complements and the ​laws of set theory. ​Various proofs ​involving sets.

3.10, 3.11

ICA 5, LaTeX practice ​with sets. End of ​lecture.


Tue, Oct 5

8:30-9:20

Lecture 12

Proofs involving sets ​continued. The power ​set.

3.10, 3.11, 3.8



Wed, Oct 6

8:30-9:20

Lecture 13

Power set, again. ​Counting sets and ​subsets. Venn ​diagrams.

3.13, 3.9, 3.12

ICA 6 (Jeopardy, end ​of class)

Worksheet 3

Fri, Oct 8

8:30-9:20

Lecture 14

More set proofs. ​Russel's paradox.

3.11, 3.1



Tue, Oct 12



Last day to drop ​classes and get a 50% ​refund




Tue, Oct 12

8:30-9:20

Lecture 15

More counting sets ​and subsets. More ​Venn diagrams. ​Inclusion-exclusion.

3.12, 3.14,



Wed, Oct 13

8:30-9:20

Lecture 16

Inclusion-exclusion ​examples. ​Introduction to ​Mathematical ​Induction.

3.14, 4.6, 4.7


Worksheet 4

Fri, Oct 15

8:30-9:20

Lecture 17

Induction and ​recursion examples. ​Strong induction.

4.1, 4.2, 4.3, 4.6, 4.7, ​4.8

ICA 7, end of class.


Tue, Oct 19

8:30-9:20

Lecture 18

Recursive definitions. ​Induction proof ​examples continued.

4.4, 4.7, 4.8

ICA 8, end of class


Wed, Oct 20

8:30-9:20

Lecture 19

Some special sums. ​Solving 1-term ​recurrences.

4.9


No worksheet

Fri, Oct 22

8:30-9:20


Term Test 1 (worth ​6.5%)




Tue, Oct 26

8:30-9:20

Lecture 20

Division algorithm. ​Floors and ceilings. ​Representing ​numbers in base b.

5.1, 5.2, 5.3



Wed, Oct 27

8:30-9:20

Lecture 21

More changing bases. ​Divisibility. Prime ​numbers. Infinitude of ​primes. Fundamental ​Theorem of ​Arithmetic.

5.5, 5.6, 5.8

ICA 9, changing base

Worksheet 5

Fri, Oct 29

8:30-9:20

Lecture 22

More FTA, Irrationality ​proofs.

5.7, 5.9,



Sun, Oct 31



Last day to withdraw ​from courses without ​penalty of failure




Tue, Nov 2

8:30-9:20

Lecture 23

gcd, lcm, Euclidean ​Algorithm

5.10, 5.11, 5.12, 5.13



Wed, Nov 3

8:30-9:20

Lecture 24

More about the ​Euclidean Algorithm ​and Integer linear ​combinations.

5.12, 5.13

ICA 10 Euclidean

Worksheet 6

Fri, Nov 5

8:30-9:20

Lecture 25

Relatively Prime. ​Modular arithmetic.

5.14, 5.15, 5.16



Tue, Nov 9

8:30-9:20

Lecture 26

Divisibility by 3 and 9. ​Cartesian product. ​Relations and their ​properties

6.1, 6.2, 6.3

ICA 11, ax+by and find ​last digit


Wed, Nov 10

8:30-9:20


Reading break (no ​classes)



No worksheet

Fri, Nov 12

8:30-9:20


Reading break (no ​classes)




Tue, Nov 16

8:30-9:20

Lecture 27

Reflexive, symmetric, ​transitive and ​antisymmetric ​relations. Equivalence ​Relations.

6.4, 6.5, 6.6, 6.7



Wed, Nov 17

8:30-9:20

Lecture 28

Equivalence relations, ​partitions

6.9, 6.10

ICA 12

Worksheet 7

Fri, Nov 19

8:30-9:20

Lecture 29

Introduction to ​functions

7.1



Tue, Nov 23

8:30-9:20

Lecture 30

Injectivity, surjectivity ​and bijectivity (Pre-​recorded, click link for ​YouTube stream)

7.3, 7.4, 7.5



Wed, Nov 24

8:30-9:20

Lecture 31

Function composition. ​The identity function ​and inverses. Perhaps ​some cardinality. ​(Pre-recorded, click ​link for YouTube ​stream)

7.6, 7.6, 7.8


No worksheet

Fri, Nov 26

8:30-9:20


Term Test 2 (worth ​6.5%)




Tue, Nov 30

8:30-9:20

Lecture 32

Introduction to ​cardinality

8.1, 8.2, 8.3

ICA 13


Wed, Dec 1

8:30-9:20

Lecture 33

Countable sets

8.4, 8.5, 8.6



Fri, Dec 3

8:30-9:20

Lecture 34

Uncountable sets

8.7, 8.8

ICA 14. At the end of ​class?

Worksheet 8

Dec 15

19:00

Final Exam

Worth 29%




Math 492/529 202101 Schedule

Date

Time

Lecture Number

Topic

Slides

Zoom ​background

Lecture Notes ​Pages

Corresponding ​Assignment (Red ​means that it ​differs from the ​chapter number)

Assignment ​Release or Due ​Dates

Mon, Jan 11

2:30-3:20

Lecture 1

Section 1.1: ​Sperner's ​Theorem

Lecture Slides

Background

1-6

1

Assignment 0 ​released ​(Crowdmark ​practice for ​bonus), ​Assignment 1 ​released, ​Optional bonus ​problems ​released

Tue, Jan 12

2:30-3:20

Lecture 2

Sperner's ​Theorem cont'd, ​Section 1.2: The ​Littlewood--​Offord Problem

Lecture Slides

Background

6-8

1


Wed, Jan 13

2:30-3:20

Lecture 3

L--O Problem ​cont'd, Section ​1.3: The LYM ​Inequalities

Lecture Slides

Background

8-11

1


Thu, Jan 14

10:30-11:20

Office Hours

Note: Special ​day and time for ​office hours in ​the first week






Mon, Jan 18

2:30-3:20

Lecture 4

Section 1.4: The ​Kruskal--Katona ​Theorem

Lecture Slides

Background

11-22

1


Wed, Jan 20

9:30-11:30

Office Hours







Wed, Jan 20

2:30-3:20

Lecture 5

Section 1.4 ​continued

Same ^

Background

11-22

1


Thu, Jan 21

2:30-3:20

Lecture 6

Section 1.4 ​continued

Same ^

Background

11-22

1


Sun, Jan 24



Last day to ​withdraw and ​get a 100% fee ​refund






Mon, Jan 25

2:30-3:20

Lecture 7

Section 1.5: The ​Harris--Kleitman ​Inequality

Lecture Slides

Background

22-23

1

Assignment 0 ​due, Assignment ​2 released

Wed, Jan 27



Last day to add ​courses






Wed, Jan 27

9:30-11:30

Office Hours







Wed, Jan 27

2:30-3:20

Lecture 8

Section 2.1: ​Intersecting ​Families

Lecture Slides

Background

26-28

2


Thu, Jan 28

2:30-3:20

Lecture 9

Section 2.2: The ​Sunflower ​Lemma, maybe ​the start of VC ​Dimension

Lecture Slides

Background

28-30

2


Sun, Jan 31








Assignment 1 ​due

Mon, Feb 1

2:30-3:20

Lecture 10

Section 2.3: VC ​Dimension

Lecture Slides

Background

30-32

2


Wed, Feb 3

9:30-10:20

Office Hours







Wed, Feb 3

2:30-3:20

Lecture 11

Appendices A, B ​and C: ​Asymptotic ​Notation, ​Probability and ​Convexity

Lecture Slides

Background

107-115

2


Thu, Feb 4

2:30-3:20

Lecture 12

Appendices ​continued

Same ^

Background

107-115

2


Fri, Feb 5

9:30-10:20

Office Hours







Mon, Feb 8

2:30-3:20

Lecture 13

Section 3.1: The ​Extremal Number ​of a Triangle

Lecture Slides

Background

35-38

3

Assignment 3 ​released

Wed, Feb 10

9:30-10:20

Office Hours







Wed, Feb 10

2:30-3:20

Lecture 14

Section 3.2: The ​Extremal Number ​of General ​Cliques

Lecture Slides

Background

38-40

3


Thu, Feb 11

2:30-3:20

Lecture 15

Section 3.3: ​Turan Density of ​General Graphs

Lecture Slides

Background

40-45

3


Fri, Feb 12

9:30-10:20

Office Hours







Sun, Feb 14








Assignment 2 ​due

Sun, Feb 14



Last day to ​withdraw and ​get a 50% fee ​refund






Mon, Feb 15


Reading Break ​(No Class)







Wed, Feb 17


Reading Break ​(No Class)







Thu, Feb 18


Reading Break ​(No Class)







Mon, Feb 22

2:30-3:20

Lecture 16

Section 3.3 ​continued

Same ^

Background

40-45

3


Wed, Feb 24

9:30-10:20

Office Hours







Wed, Feb 24

2:30-3:20

Lecture 17

3.3 continued, ​Section 3.4: ​Extremal ​Numbers of ​Bipartite Graphs

Lecture Slides

Background

45-47

3


Thu, Feb 25

2:30-3:20

Lecture 18

Section 3.5: ​Better Bounds ​for Even Cycles

Lecture Slides

Background

47-49

3


Fri, Feb 26

9:30-10:20

Office Hours







Sat, Feb 27








Assignments 4, 5 ​and 6 released

Sun, Feb 28



Last day to ​withdraw without ​penalty of failure






Mon, Mar 1

2:30-3:20

Lecture 19

Section 4.1: ​Stability for ​Turan's Theorem

Lecture Slides

Background

53-55

4


Wed, Mar 3

9:30-10:20

Office Hours







Wed, Mar 3

2:30-3:20

Lecture 20

Section 4.3: ​Sharper ​Supersaturation ​for Triangles

Lecture Slides

Background

57-58

4


Thu, Mar 4

2:30-3:20

Lecture 21

Section 4.4: ​Sharper ​Supersaturation ​for Quadrangles

Lecture Slides

Background

58-60

4


Fri, Mar 5

9:30-10:20

Office Hours







Sun, Mar 7








Assignment 3 ​due

Mon, Mar 8

2:30-3:20

Lecture 22

Section 4.5: ​Sharper ​Supersaturation ​for Even Cycles

Lecture Slides

Background

60-63

4


Wed, Mar 10

9:30-11:20

Office Hours ​(Extended)







Wed, Mar 10

2:30-3:20

Lecture 23

Section 4.5 ​continued

Same^

Background

60-63

4


Thu, Mar 11

2:30-3:20

Lecture 24

Section 4.2: ​Approximate ​Supersaturation ​for General ​Graphs

Lecture Slides

Background

55-57

4


Fri, Mar 12

9:30-10:20

Office Hours ​(Cancelled)







Mon, Mar 15

2:30-3:20

Lecture 25

Section 5.1: ​Regular Pairs ​and Counting

Lecture Slides

Background

68-71

5


Wed, Mar 17

9:30-10:20

Office Hours







Wed, Mar 17

2:30-3:20

Lecture 26

Section 5.2: The ​Regularity and ​Triangle Removal ​Lemmas

Lecture Slides

Background

71-76

5


Thu, Mar 18

2:30-3:20

Lecture 27

Section 5.2 ​continued

Same^

Background

71-76

5


Fri, Mar 19

9:30-10:20

Office Hours







Sun, Mar 21








Assignment 4 ​due

Mon, Mar 22

2:30-3:20

Lecture 28

Section 5.3: ​Proof of the ​Regularity ​Lemma

Lecture Slides

Background

76-82

5


Wed, Mar 24

9:30-10:20

Office Hours







Wed, Mar 24

2:30-3:20

Lecture 29

Section 5.3 ​continued

Same^

Background

76-82

5


Thu, Mar 25

2:30-3:20

Lecture 30

Section 5.3 ​continued

Same^

Same^

76-82

5


Fri, Mar 26

9:30-10:20

Office Hours







Mon, Mar 29

2:30-3:20

Lecture 31

Section 6.1: ​Independent ​Sets in Triangle-​Free Graphs

Lecture Slides

Background

85-88

6


Wed, Mar 31

9:30-10:20

Office Hours







Wed, Mar 31

2:30-3:20

Lecture 32

6.1 continued, ​Section 6.2: ​Counting ​Independent ​Sets in Regular ​Graphs

Lecture Slides

Background

88-92

6


Thu, Apr 1

2:30-3:20

Lecture 33

6.2 continued, ​Introduction to ​Entropy

Lecture Slides

Background

88-92, 92-98

6


Fri, Apr 2

9:30-10:20

Office Hours

Cancelled (Good ​Friday)






Sun, Apr 4








Assignment 5 ​due

Mon, Apr 5


Easter Monday ​(No Class)







Wed, Apr 7

9:30-10:20

Office Hours







Wed, Apr 7

2:30-3:20

Lecture 34

Entropy ​continued, ​Section 6.3: ​Permanents and ​Counting Perfect ​Matchings

Lecture Slides

Background

92-98

6


Thu, Apr 8

2:30-3:20

Lecture 35

Section 6.3 ​continued

Same^

Background

92-98

6


Fri, Apr 9

9:30-10:20

Office Hours







Mon, Apr 12

2:30-3:20

Lecture 36

Section 6.4: ​Homomorphism ​Density of Trees

Lecture Slides

Background

98-100

6

Bonus problems ​due

Thu, Apr 15


Exam Period (No ​Class)






Project due

Sun, Apr 18


Exam Period (No ​Class)






Assignment 6 ​due

TBA


Exam Period (No ​Class)

Oral Final Exam






Math 222 202109 Schedule

Date. ​Purple ​means past

Time

Lecture ​Number

Topic

Sections of Textbook

Correspond​ing ​Assignment

Correspond​ing Test

Correspond​ing Quiz

Assignment ​Release ​and Due ​Dates

Quiz ​Release ​and Due ​Dates

YouTube Videos from ​Last Year's Course (and ​Other Sources)

Wed, Sep 8

1:30-2:20

Lecture 1

Introductio​n to the ​course, ​counting ​rules. ​Functions ​and strings.

Chapter 1

Section 2.1

1

1

1

Assignment ​1 released


Video


Fri, Sep 10

1:30-2:20

Lecture 2

More on ​functions ​and strings. ​Permutatio​ns and ​combinatio​ns

Section 2.2

Section 2.3

1

1

1



Video


Tue, Sep 14

1:30-2:20

Lecture 3

More on ​permutatio​ns and ​combinatio​ns. ​Examples. ​Facts about ​binomial ​coefficients​.

Section 2.3

Section 2.5

1

1

1



Video


Wed, Sep ​15

1:30-2:20

Lecture 4

Binomial ​coefficients ​are ​everywhere​!

Section 2.5


1

1

1



Video

See also

Fri, Sep 17

1:30-2:20

Lecture 5

Combinator​ial proofs. ​Pascal's ​identity.

Section 2.4

Section 3.4

1

1

1



Video


Tue, Sep 21



Last day to ​drop ​courses ​and get a ​100% fee ​refund










Tue, Sep 21

1:30-2:20

Lecture 6

Combinator​ial proofs ​continued. ​The ​Pigeonhole ​Principle

Section 2.4

Section 4.1

1

1

1



Video

https://ww​w.youtube.​com/watch​?​v=W0vHpk​SyxVU&t=4​56s

Wed, Sep ​22

1:30-2:20

Lecture 7

A little bit ​more ​Pigeonhole. ​The ​Binomial ​Theorem ​and ​application​s.

Section 4.1

Section 2.6

1

1

1



Video


Fri, Sep 24



Last day to ​add ​courses










Fri, Sep 24

1:30-2:20

Lecture 8

The ​Binomial ​Theorem ​continued. ​Multinomial ​coefficients ​and ​repetitions

Section 2.6

Section 2.7

2

1

1

Assignment ​2 released


Video

Video

Tue, Sep ​28

1:30-2:20

Lecture 9

A few more ​complicate​d examples ​using ​multinomial ​coefficients​. ​Introductio​n to ​Inclusion-​Exclusion.

Section 2.7

Section 7.1

2

1

1

Assignment ​1 due, ​worth 7%

Quiz 1 ​released

Video


Wed, Sep ​29

1:30-2:20

Lecture 10

Principle of ​Inclusion-​Exclusion

Section 7.1

Section 7.2

2

1

N/A



Video


Fri, Oct 1

1:30-2:20

Lecture 11

Counting ​derangeme​nts

Section 7.3

Section 7.4

2

1

N/A



Video


Tue, Oct 5

1:30-2:20

Lecture 12

Counting ​surjections. ​Maybe a bit ​more ​derangeme​nts stuff, ​too.

Section 7.3

Section 7.4

2

1

N/A


Quiz 1 due, ​worth 3%

Video


Wed, Oct 6

1:30-2:20

Lecture 13

Graphs and ​digraphs, ​isomorphis​m, ​Handshakin​g Lemma

Section 5.1


3

2

2

Assignment ​3 released


Video

See also

Fri, Oct 8

1:30-2:20

Test 1, ​Worth 11%

Link to last ​year's test ​(Note that ​the test last ​year was ​1.5 hours ​long and ​open book. ​Therefore, ​the test ​this year ​will have a ​different ​format and ​different ​types of ​questions.)










Tue, Oct 12



Last day to ​drop ​courses ​and get a ​50% fee ​refund










Tue, Oct 12

1:30-2:20

Lecture 14

Graph ​theory ​basics ​continued. ​Multigraphs​.

Section 5.1

Section 5.2

3

2

2

Assignment ​2 due, ​worth 7%


Video


Wed, Oct ​13

1:30-2:20

Lecture 15

Eulerian ​circuits

Section 5.2

Section 5.3

3

2

2



Video

See also

Fri, Oct 15

1:30-2:20

Lecture 16

A bit more ​Eulerian ​stuff. ​Hamiltonian ​cycles

Section 5.3


3

2

2



Video


Tue, Oct 19

1:30-2:20

Lecture 17

Trees

Section 5.1


3

2

2



Video


Wed, Oct ​20

1:30-2:20

Lecture 18

Graph ​colouring

Section 5.4


3

2

2



Video


Fri, Oct 22

1:30-2:20

Lecture 19

Bipartite ​graphs. ​Planar ​graphs

Section 5.5


3

2

2


Quiz 2 ​released

No video ​from me :(

Try this one

Tue, Oct 26

1:30-2:20

Lecture 20

Maybe a bit ​more ​planarity. ​Binary ​relations ​and ​equivalenc​e relations

Section B.4

Section ​B.13

N/A

2

N/A



No video ​from me :(

Try this one

Wed, Oct ​27

1:30-2:20

Lecture 21

More about ​relations. ​Partial ​orders, ​Hasse ​diagrams

Section 6.1


N/A

2

N/A



No video ​from me :(

Try this one

Fri, Oct 29

1:30-2:20

Lecture 22

Generating ​functions

Section 8.1

Section 8.2

4

3

3

Assignment ​4 released

Quiz 2 due, ​worth 3%

Video


Sun, Oct 31



Last day to ​drop ​courses ​without ​penalty of ​failure










Tue, Nov 2

1:30-2:20

Lecture 23

Using ​generating ​functions to ​solve ​counting ​problems

Section 8.2


4

3

3

Assignment ​3 due, ​worth 7%


Video


Wed, Nov 3

1:30-2:20

Test 2, ​Worth 11%

Link to ​practice ​questions










Fri, Nov 5

1:30-2:20

Lecture 24

Using ​generating ​functions to ​solve ​counting ​problems, ​continued.

Section 8.2


4

3

3



Video


Tue, Nov 9

1:30-2:20

Lecture 25

Generating ​functions ​and integer ​partitions

Section 8.5


4

3

3



Video


Wed, Nov ​10



Reading ​break (no ​classes)










Fri, Nov 12













Tue, Nov 16

1:30-2:20

Lecture 26

Partitions ​of integers ​continued. ​Newton's ​binomial ​theorem.

Section 8.5

Section 8.3

4

3

3



Video 1

Video 2

Wed, Nov ​17

1:30-2:20

Lecture 27

An ​application ​of ​Newton's ​binomial ​theorem. ​Maybe ​some ​basics of ​recurrence ​relations.

Section 8.3

Section 8.4

4

3

3



Video


Fri, Nov 19

1:30-2:20

Lecture 28

Recurrence ​relations ​(re-​explaining ​linear, ​homogeneo​us, etc). ​Phrasing ​problems ​as ​recurrence ​relations ​and solving ​simple ​ones. ​Recurrence ​relation ​terminology​.

Section 9.1

Levin, 2.4

5

3

3

Assignment ​5 released


Video


Tue, Nov ​23

1:30-2:20

Lecture 29

More ​simple ​linear ​recurrence ​relations, ​and how to ​solve them ​(Pre-​recorded, ​click for ​YouTube ​link)

Section 9.1

Levin, 2.4

5

3

3

Assignment ​4 due, ​worth 7%

Quiz 3 ​released

Video


Wed, Nov ​24

1:30-2:20

Lecture 30

Solving ​linear ​recurrence ​relations ​(Pre-​recorded, ​click for ​YouTube ​link)

Levin, 2.4


5

3

N/A



Video 1

Video 2

Fri, Nov 26

1:30-2:20

Lecture 31

Solving ​linear ​recurrence ​relations ​(continued)​. Using ​generating ​functions to ​solve ​recurrence ​relations ​(Pre-​recorded, ​click for ​YouTube ​link)

Levin, 2.4

Section 9.6

5

3

N/A



Video 1

Video 2

Tue, Nov ​30

1:30-2:20

Lecture 32

Using ​generating ​functions to ​solve ​recurrence ​relations, ​continued

Levin, 2.4

Section 9.6

5

3

N/A


Quiz 3 due, ​worth 3%

Video 1

Video 2

Wed, Dec 1

1:30-2:20

Lecture 33

A non-​linear ​recurrence ​and ​Catalan ​numbers

Section 2.5

Section 9.7

5

3

N/A



Video


Fri, Dec 3

1:30-2:20

Test 3, ​Worth 11%

Link to ​practice ​questions










Tue, Dec 7









Assignment ​5 due, ​worth 7%




Mon, Dec ​13

4:00-9:20

Review ​Session

On Zoom. ​See ​Brightspac​e for Link.










Dec 17

2:00 PM

Final Exam

Worth 23%










Math 222 202101 Schedule

Date

Time

Lecture ​Number

Topic

Slides

Zoom ​Background

Chapters/Sections of ​Textbook

Correspondi​ng ​Assignment

Correspondi​ng Test

Assignment ​Release and ​Due Dates

Quiz Release ​and Due ​Dates

Mon, Jan 11

11:30-12:50

Lecture 1

Introduction ​to the ​course, ​counting ​rules, ​functions, ​strings

Lecture ​Slides

Background

Chapter 1

Section 2.1

1

1

Assigment 0 ​(optional ​Crowdmark ​practice for ​bonus) ​released, ​Assignment ​1 released


Thu, Jan 14

11:30-12:50

Lecture 2

Permutation​s and ​combination​s

Lecture ​Slides

Background

Section 2.2

Section 2.3

1

1


Q1 released

Fri, Jan 15

11:30-12:20

Office Hours

Note: ​Special day ​and time for ​office hours ​in the first ​week









Mon, Jan 18

11:30-12:50

Lecture 3

Binomial ​coefficients ​are ​everywhere, ​the ​Pigeonhole ​Principle

Lecture ​Slides

Background

Section 2.5

Section 4.1

1

1



Wed, Jan 20

12:30-2:20

Office Hours










Thu, Jan 21

11:30-12:50

Lecture 4

Combinatori​al proofs, ​some ​identities ​including ​Pascal's

Lecture ​Slides

Background

Section 2.4

Section 3.4

1

1


Q1 due, Q2 ​released

Sun, Jan 24



Last day to ​withdraw ​and get a ​100% fee ​refund









Mon, Jan 25

11:30-12:50

Lecture 5

The Binomial ​Theorem ​and ​applications

Lecture ​Slides

Background

Section 2.6


2

1

Assignment ​0 due, ​Assignment ​2 released


Wed, Jan 27



Last day to ​add courses









Wed, Jan 27

12:30-2:20

Office Hours










Thu, Jan 28

11:30-12:50

Lecture 6

Multinomial ​coefficients ​and ​repetitions

Lecture ​Slides

Background

Section 2.7


2

1


Q2 due, Q3 ​released

Sun, Jan 31










Assignment ​1 due


Mon, Feb 1

11:30-12:50

Lecture 7

Principle of ​Inclusion-​Exclusion

Lecture ​Slides

Background

Section 7.1

Section 7.2

2

1



Wed, Feb 3

12:30-2:20

Office Hours










Thu, Feb 4

11:30-12:50

Lecture 8

Counting ​surjections ​and ​derangemen​ts

Lecture ​Slides

Background

Section 7.3

Section 7.4

2

1


Q3 due, Q4 ​released

Mon, Feb 8

11:30-12:50

Lecture 9

Graphs and ​digraphs, ​isomorphism​, ​Handshakin​g Lemma

Lecture ​Slides

Background

Section 5.1


3

2

Assignment ​3 released


Wed, Feb 10

12:30-2:20

Office Hours










Thu, Feb 11

11:30-12:25 ​plus 25 ​minutes for ​submission

Test 1

The official ​time for the ​test is ​11:30am-​12:25pm. ​There is an ​extra 25 ​minutes to ​allow time to ​submit the ​test online. ​The ​submission ​is due by ​12:50pm.

Slide

Background







Sun, Feb 14



Last day to ​withdraw ​and get a ​50% fee ​refund









Mon, Feb 15


Reading ​Break (No ​Class)










Thu, Feb 18


Reading ​Break (No ​Class)










Mon, Feb 22

11:30-12:50

Lecture 10

Multigraphs ​and Eulerian ​circuits

Lecture ​Slides

Background

Section 5.2

Section 5.3

3

2


Q4 due, Q5 ​released

Wed, Feb 24

12:30-2:20

Office Hours










Wed, Feb 24










Assignment ​2 due


Thu, Feb 25

11:30-12:50

Lecture 11

Hamiltonian ​cycles, trees

Lecture ​Slides

Background

Section 5.3

Section 5.1

3

2



Sun, Feb 28



Last day to ​withdraw ​without ​penalty of ​failure









Mon, Mar 1

11:30-12:50

Lecture 12

Graph ​colouring

Lecture ​Slides

Background

Section 5.4


3

2


Q5 due, Q6 ​released

Wed, Mar 3

12:30-2:20

Office Hours










Thu, Mar 4

11:30-12:50

Lecture 13

Planar ​graphs

Lecture ​Slides

Background

Section 5.5


3

2



Mon, Mar 8

11:30-12:50

Lecture 14

Binary ​relations, ​equivalence ​relations, ​partial ​orders, ​Hasse ​diagrams

Lecture ​Slides

Background

Section B.4, ​Section B.13

Section 6.1

N/A

2


Q6 due, Q7 ​released

Wed, Mar 10

12:30-2:20

Office Hours










Thu, Mar 11

11:30-12:50

Lecture 15

Generating ​functions

Lecture ​Slides

Background

Section 8.1

Section 8.2

4

3

Assignment ​4 released


Thu, Mar 11



Deadline to ​tell me if you ​want to do ​the evening ​version of ​Test 2









Sun, Mar 14










Assignment ​3 due


Mon, Mar 15

11:30-12:50

Lecture 16

Using ​generating ​functions to ​solve ​counting ​problems

Lecture ​Slides

Background

Section 8.2


4

3


Q7 due, Q8 ​released

Wed, Mar 17

12:30-2:20

Office Hours










Thu, Mar 18

11:30am-​12:50pm

Test 2

The test ​starts at ​11:30am. ​The ​submission ​is due by ​12:50pm.









Thu, Mar 18

8:30pm-​9:50pm

Test 2 ​(Evening ​Version)

The test ​starts at ​8:30pm. The ​submission ​is due by ​9:50pm.









Mon, Mar 22

11:30-12:50

Lecture 17

Using ​generating ​functions to ​solve ​counting ​problems, ​continued. ​Generating ​functions ​and integer ​partitions

Lecture ​Slides

Background

Section 8.2

Section 8.5

4

3



Wed, Mar 24

12:30-2:20

Office Hours










Thu, Mar 25

11:30-12:50

Lecture 18

Partitions of ​integers ​continued. ​Newton's ​Binomial ​Theorem ​and an ​application

Lecture ​Slides

Background

Section 8.3

Section 8.4

4

3


Q8 due, Q9 ​released

Mon, Mar 29

11:30-12:50

Lecture 19

Phrasing ​problems as ​recurrence ​relations, ​some simple ​linear ​recurrence ​relations

Lecture ​Slides

Background

Section 9.1

Levin, 2.4

5

3

Assignment ​5 released


Wed, Mar 31

12:30-2:20

Office Hours










Thu, Apr 1

11:30-12:50

Lecture 20

Solving ​linear ​recurrence ​relations

Lecture ​Slides

Background

Levin, 2.4


5

3


Q9 due, Q10 ​released

Sat, Apr 3










Assignment ​4 due


Mon, Apr 5


Easter ​Monday (No ​Class)










Wed, Apr 7

12:30-2:20

Office Hours










Thu, Apr 8

11:30-12:50

Lecture 21

Solving ​linear ​recurrence ​relations ​(continued). ​Using ​generating ​functions to ​solve ​recurrence ​relations

Lecture ​Slides

Background

Levin, 2.4

Section 9.6

5

3



Mon, Apr 12

11:30-12:50

Lecture 22

A non-linear ​recurrence ​and Catalan ​numbers

Lecture ​Slides

Background

Section 2.5

Section 9.7

5

3


Q10 due, Q11 ​released

Sun, Apr 18


Exam Period ​(No Class)








Assignment ​5 due


Mon, Apr 19


Exam Period ​(No Class)









Q11 due

Mon, Apr 19



Deadline to ​tell me if you ​want to do ​the evening ​version of ​Test 3









Mon, Apr 26

9:00am-​10:20am

Test 3

The test ​starts at ​9:00am. The ​submission ​is due by ​10:20am.









Mon, Apr 26

8:30pm-​9:50pm

Test 3 ​(Evening ​Version)

The test ​starts at ​8:30pm. The ​submission ​is due by ​9:50pm.