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The prerequisite to the course Discrete Mathematics: Open Doors to Great Careers 2.

Would you like to learn a mathematics subject that is crucial for many highdemand lucrative career fields such as:
If you're looking to gain a solid foundation in Discrete Mathematics, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on discrete mathematics or a complete beginner who needs to learn Discrete Mathematics for the first time, this online course is for you.
Why you should take this online course: You need to refresh your knowledge of discrete mathematics for your career to earn a higher salary. You need to learn discrete mathematics because it is a required mathematical subject for your chosen career field such as computer science or electrical engineering. You intend to pursue a masters degree or PhD, and discrete mathematics is a required or recommended subject.
Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, four years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.
In this course, I cover core topics such as:
After taking this course, you will feel CAREFREE AND CONFIDENT. I will break it all down into bitesized nobrainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.
Practice problems are provided for you, and detailed solutions are also provided to check your understanding.
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Section 1: Introduction  

Lecture 1 
Introduction Lecture
Preview

03:05  
Section 2: Propositional Logic  
Lecture 2  07:28  
In this lecture, we introduce the notions of a statement, statement variables, the negation symbol, and a truthtable. Students will be introduced to the building blocks of logic. 

Lecture 3  07:59  
The logical symbols of conjunction and disjunction are introduced. Students will learn how to evaluate the truthvalue of statements involving conjunction and disjunction. 

Lecture 4  10:50  
The conditional symbol and the biconditional symbol are introduced. Students will learn how to evaluate the truthvalues of conditional and biconditional statements. 

Lecture 5  08:53  
The notion of a statement form is introduced. Students will learn how to find the truthtables for statement forms. 

Lecture 6 
Problem Set: Statement Forms

00:01  
Lecture 7  14:10  
The notion of logical equivalence is introduced. Students will learn how to show that two statement forms are logically equivalent and how to show that two statement forms are not logically equivalent. 

Lecture 8 
Problem Set: Logical Equivalence

00:01  
Lecture 9  07:18  
In this lecture, the notion of a tautology and the notion of a contradiction are introduced. Students will learn how to prove logical equivalences involving tautologies and contradictions. 

Lecture 10 
Problem Set: Tautology and Contradiction

00:01  
Lecture 11  15:27  
In this lecture, we will look at a list of logical equivalences that can be used to prove other logical equivalences. We will also learn about the contrapositive of a conditional statement. Students will learn how to use the laws in the list of logical equivalences to prove other logical equivalences. 

Lecture 12 
Problem Set: Logical Equivalences

00:01  
Lecture 13  08:55  
In this lecture, the notions of argument, argument form, and validity are introduced. Students will learn how to prove that an argument form is valid and how to prove that an argument form is invalid. 

Lecture 14 
Problem Set: Arguments

00:00  
Lecture 15  06:32  
The notion of a rule of inference is introduced. Students will learn about some important rules of inference. 

Lecture 16  10:34  
In this lecture, we go through a list of rules of inference and apply them in constructing arguments. Students will learn how to construct arguments using rules of inference. 

Lecture 17 
Problem Set: Rules of Inference

00:01  
Section 3: Predicate Logic  
Lecture 18  10:28  
In this lecture, we introduce the notions of a predicate symbol, a variable, constant symbols, predicates, the domain of a variable, and the truthset of a predicate. Students will be introduced to the building blocks of predicate logic. 

Lecture 19  06:02  
Students will learn how to find the truthset of a predicate. 

Lecture 20 
Problem Set: Truthset

00:00  
Lecture 21  09:12  
The universal quantifier symbol is introduced. Students will learn how to prove and disprove statements involving the universal quantifier. 

Lecture 22  08:54  
The existential quantifier symbol is introduced. Students will learn how to prove and disprove statements involving the existential quantifier. 

Lecture 23  09:08  
The notion of a universal conditional statement is introduced. Students will learn how to prove and disprove universal conditional statements. 

Lecture 24 
Problem Set: Quantifiers

00:00  
Lecture 25  12:01  
Students will learn how to find the negation of a quantified statement. 

Lecture 26 
Problem Set: Negations and Quantified Statements

00:01  
Lecture 27  07:23  
Students are introduced to statements involving multiple quantifiers. 

Lecture 28  07:05  
Students will learn how negations of multiplyquantified statements work. 

Lecture 29 
Problem Set: Multiple Quantifiers

00:01  
Lecture 30  13:09  
The rules of inference universal instantiation, universal modus ponens, universal modus tollens, and universal generalization are introduced. Students will learn how rules of inference involving the universal quantifier work. 

Lecture 31  04:21  
The rules of inference existential instantiation and existential generalization are introduced. Students will learn how rules of inference involving the existential quantifier work. 

Lecture 32 
Problem Set: Rules of Inference Involving Quantifiers

00:01  
Lecture 33  11:00  
Students will learn how to construct arguments using rules of inference involving quantifiers. 

Lecture 34 
Problem Set: Constructing Arguments Involving Quantified Statements

00:01  
Section 4: Proofs  
Lecture 35  08:31  
Students will be able to prove existential statements by providing an example. Students will also learn how to disprove universal statements by providing a counterexample. 

Lecture 36  10:00  
Students will learn how to prove universal statements by using the method of exhaustion and by using the method of direct proof. 

Lecture 37 
Problem Set: Methods of Proof

00:01  
Lecture 38  07:13  
Students will be able to perform proofs by contradiction. 

Lecture 39  08:38  
Students will be able to perform proofs by contraposition. 

Lecture 40 
Problem Set: Proofs by Contradiction and by Contraposition

00:02  
Section 5: Mathematical Induction  
Lecture 41  16:37  
Students will be able to construct proofs using mathematical induction. 

Lecture 42 
Problem Set: Mathematical Induction

00:01  
Lecture 43  04:27  
Students will be able to construct proofs using strong induction. 

Lecture 44  11:03  
An example of a proof by strong induction is provided. 

Lecture 45  10:17  
An additional example of a proof by strong induction is provided. 

Lecture 46 
Problem Set: Strong Induction

00:01  
Section 6: Concluding Letter  
Lecture 47 
Concluding Letter

00:21  
Lecture 48 
Bonus Lecture

00:10 
Hi there! My name is Richard Han. I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International. My expertise includes calculus and linear algebra. I am an instructor on Udemy for the courses Philosophy of Language: Solidify Critical Thinking Skills and Linear Algebra for Beginners: Open Doors to Great Careers.