1. Ch 1. Sets & Counting

1.5hr

1.1.1. Basics of Sets7 min

1.1.2. Example: Basics of Sets5 min

1.1.3. Example: Elements in a Set5 min

1.1.4. Practice: Elements in a Set5 min

1.2.1. Counting Elements & Tables4 min

1.2.2. Example: Counting Elements w/ Tables2 min

1.2.3. Example: Counting Elements w/ Tables3 min

1.2.4. Practice: Counting Elements w/ Tables5 min

1.2.5. Example: Counting Elements in Word Problems4 min

1.2.6. Practice: Counting Elements in Word Problems3 min

1.3.1. Counting Elements & Tree Diagrams4 min

1.3.2. Example: Tree Diagrams3 min

1.3.3. Example: Counting Elements w/ Trees8 min

1.3.4. Practice: Counting Elements w/ Trees7 min

1.4.1. Fundamental Counting Principle (FCP)*4 min

1.4.2. Example: Fundametal Counting Principle5 min

1.4.3. Practice: Fundamental Counting Principle2 min

1.4.4. Practice: Fundamental Counting Principle w/ Cases5 min

1.5.1. Subsets1 min

1.5.2. Example: Subsets3 min

1.5.3. Practice: Subsets3 min

1.5.4. Example: Subsets*3 min

1.Q. Counting Sets Checkpoint Quiz (give yourself ~30 minutes)9 Qns

1.P.1. Practice Question

1.P.2. Practice Question

1.P.3. Practice Question

1.P.4. Practice Question

1.P.5. Practice Question

1.P.6. Practice Question

1.P.7. Practice Question

2. Ch 1. Permutations & Combinations

54min

2.1.1. Factorial Symbol (!)3 min

2.1.2. Permutations (Extension of FCP)3 min

2.1.3. Example: Permutation5 min

2.1.4. Example: Permutations3 min

2.1.5. Practice: Permutations2 min

2.1.6. Example: Permutation w/ Repeated Objects1 min

2.1.7. Practice: Permutation w/ Repeated Objects4 min

2.2.1. Combinations5 min

2.2.2. Example: Combination Notation3 min

2.2.3. Practice: Combination Notation3 min

2.2.4. Example: Combinations6 min

2.2.5. Practice: Combinations3 min

2.2.6. Example: Splitting up a Group w/ Combination2 min

2.3.1. Deck of Cards Questions1 min

2.3.2. Example: Combinations w/ Cards3 min

2.3.3. Practice: Combinations w/ Cards2 min

2.4.1. Example: Mixed Combination & Permutation2 min

2.4.2. Practice: Mixed Combination & Permutation2 min

2.Q. Permutation Checkpoint Quiz (give yourself ~ 30 minutes)15 Qns

3. Ch 2. Intro to Probability

1.2hr

3.1.1. Definitions: Experiment, Outcome, Sample Space7 min

3.1.2. Example: Equiprobably Sample Space2 min

3.1.3. Example: Sample Space2 min

3.1.4. Practice: Sample Space4 min

3.2.1. Properties of Probability5 min

3.2.2. Example: Properties of Probability3 min

3.2.3. Practice: Properties of Probability3 min

3.2.4. Practice: Properties of Probability3 min

3.2.5. Probability Table (very useful)1 min

3.2.6. Example: Probability Using Table2 min

3.2.7. Practice: Probability Using Table2 min

3.2.8. Example: Probability Using Table3 min

3.2.9. Practice: Probability Using Table3 min

3.3.1. Calculating Probability4 min

3.3.2. Example: Equiprobable Sample Space2 min

3.3.3. Example: Line Permutation & Probability2 min

3.3.4. Example: Circle Permutation & Probability2 min

3.3.5. Practice: Circle Permutation & Probability3 min

3.3.6. Example: Dice & Probability4 min

3.3.7. Practice: Combination & Probability2 min

3.3.8. Example: Cards & Probability4 min

3.3.9. Practice: Cards & Probability4 min

3.3.10. Example: Distribution (Labelling) & Probability2 min

3.3.11. Example: Free Distributions & Probability2 min

3.Q. Checkpoint Quiz: Intro to Probability (~35-50 mins)12 Qns

3.P.1. Practice: Sample Space

3.P.2. Practice: Free Distribution & Probability

3.P.3. Practice: Cards & Probability

3.P.4. Practice: Independent Events

3.P.5. Practice: Sample Space

4. Ch 2. Conditional Probability & Trees

1.2hr

4.1.1. Conditional Probability4 min

4.1.2. Example: Conditional Probability & Table3 min

4.1.3. Practice: Conditional Probability4 min

4.1.4. Example: Dice & Conditional Probability2 min

4.1.5. Example: Cards & Conditional Probability4 min

4.1.6. Practice: Cards & Conditional Probability3 min

4.1.7. Practice: Cards & Conditional Probability4 min

4.1.8. Example: Circle Permutation & Conditional Probability4 min

4.1.9. Practice: Circle Permutation & Conditional Probability4 min

4.2.1. Stochastic Process and Bayes’ Theorem3 min

4.2.2. Example: Stochastic Process6 min

4.2.3. Practice: Stochastic Process4 min

4.2.4. Example: Bayes' Theorem4 min

4.2.5. Practice: Bayes' Theorem6 min

4.2.6. Example: Bayes' Theorem8 min

4.2.7. Practice: Bayes' Theorem5 min

4.Q. Checkpoint Quiz: Conditional Probability & Trees (~40-45 mins)10 Qns

4.P.1. Practice: Conditional Probability

5. Ch 3. Discrete Random Variables

1.3hr

5.1.1. Random Variable & Probability Distribution Function6 min

5.1.2. Example: PDF3 min

5.1.3. Practice: PDF4 min

5.1.4. Example: PDF6 min

5.1.5. Practice: PDF4 min

5.2.1. Expected Value

E(x)

or Mean

\mu

4 min

5.2.2. Example: Expected Value3 min

5.2.3. Practice: Expected Value2 min

5.2.4. Example: Expected Value3 min

5.2.5. Practice: Expected Value2 min

5.3.1. Bernoulli Trials6 min

5.3.2. Example: Bernoulli Trials5 min

5.3.3. Example: Bernoulli Trials4 min

5.3.4. Practice: Bernoulli Trials4 min

5.3.5. Example: Bernoulli & Conditional Probability4 min

5.3.6. Practice: Bernoulli Trials & Conditional Probability5 min

5.4.1. Bionomial Random Variable4 min

5.4.2. Example: Binomial RV3 min

5.4.3. Practice: Binomial RV2 min

5.4.4. Example: Binomial RV2 min

5.4.5. Practice: Binomial RV2 min

5.Q. Checkpoint Quiz: Discrete Random Variable (Give yourself ~25-35 minutes)4 Qns

6. Ch 4. Systems of Linear Equations (SLEs) (Linear Systems)

1.4hr

6.1.1. Basics of Systems of Linear Equations8 min

6.1.2. Example3 min

6.1.3. Practice2 min

6.1.4. Practice3 min

6.2.1. Augmented Matrix3 min

6.3.1. Echelon Forms5 min

6.4.1. Rank of a Matrix5 min

6.4.2. Example3 min

6.4.3. Practice38 sec

6.4.4. Practice1 min

6.5.1. Reducing a Matrix5 min

6.6.1. Solving Linear Systems5 min

7. Ch 4. Matrices

54min

8. Ch 5. Linear Inequalities in 2 Variables

46min

8.1.1. Solving Linear Inequalities in Two Variables5 min

8.1.2. Example5 min

8.1.3. Practice Level 13 min

8.1.4. Practice Level 36 min

8.2.1. Systems of Linear Inequalities4 min

8.2.2. Example9 min

8.2.3. Practice3 min

8.2.4. Practice5 min

8.2.5. Example: Graphing a System of Linear Inequalities5 min

8.2.6. Practice: Graphing a System of Linear Inequalities3 min

9. Ch 5. Linear Programming

36min

9.1.1. Optimizing a Function 3 min

9.1.2. Example: Setting Up LPP4 min

9.1.3. Example: Solving a Linear Programming Problem6 min

9.1.4. Practice: Solving a Linear Programming Problem2 min

9.1.5. Isoprofit Lines3 min

9.1.6. Example: LPP (with Isoprofit Lines)12 min

9.1.7. Practice: LPP (Use Isoprofit Lines)5 min

9.Q. Checkpoint Quiz4 Qns

10. Ch 6. Markov Chain

1.4hr

10.1.1. Markov Chains7 min

10.1.2. Example: A 2-state Markov chain5 min

10.1.3. Example: Markov Chain 1st and 2nd Stage3 min

10.1.4. Example6 min

10.1.5. Practice5 min

10.1.6. Practice: Markov Chains Problem5 min

10.1.7. Practice: Markov Chain With 3 States4 min

10.2.1. Regular Markov Chains4 min

10.2.2. Example: Regular Markov Chains3 min

10.2.3. Practice: Regular Markov Chains4 min

10.2.4. Markov Chains and Stationary States4 min

10.2.5. Finding the Stationary State2 min

10.2.6. Example: Finding a Stationary State5 min

10.2.7. Practice: Finding a Stationary State6 min

10.3.1. Absorbing Markov Chains3 min

10.3.2. Example: Absorbing Markov Chains5 min

10.3.3. Limiting Matrix for Absorbing Markov Chains3 min

10.3.4. Example: Limiting Matrix for Absorbing Markov Chains6 min

10.3.5. Practice: Absorbing Markov Chains3 min

MATH 151

Course Overview

1. Ch 1. Sets & Counting

2. Ch 1. Permutations & Combinations

3. Ch 2. Intro to Probability

4. Ch 2. Conditional Probability & Trees

5. Ch 3. Discrete Random Variables

6. Ch 4. Systems of Linear Equations (SLEs) (Linear Systems)

7. Ch 4. Matrices

8. Ch 5. Linear Inequalities in 2 Variables

9. Ch 5. Linear Programming

10. Ch 6. Markov Chain

Term Test 2 Overview

Course Notes