Please confirm that you want to add Discrete Mathematics: Open Doors to Great Careers 2 to your Wishlist.
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The sequel to the course Discrete Mathematics: Open Doors to Great Careers.
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Would you like to learn a mathematics subject that is crucial for many high-demand 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 CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer 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.
30 day full refund if not satisfied.
Grab a cup of coffee and start listening to the first lecture. I, and your peers, are here to help. We're waiting for your insights and questions! Enroll now!
Students will be introduced to the notions of set, element, set equality, subset, and proper subset.
Students will learn how to find the union, intersection, difference, and complements of sets.
Students will learn how to find the union of any number of sets and the intersection of any number of sets.
The notion of a partition is introduced.
Students will be able to determine if a collection of sets forms a partition of a given set.
The notion of the power set of a set is introduced.
Students will be able to find the power set of a given set.
The notion of the Cartesian product of a collection of sets is introduced.
Students will be able to find the Cartesian product of a collection of sets.
In this lecture, students are introduced to set identities.
Students will be able to prove set identities.
The notion of a function is introduced.
Students will understand what the domain and range of a function are, and students will understand what the image of an element is and what the preimage of an element is.
In this lecture, we look at some examples of functions, including the floor function.
Students will be able to find the domain and range of a function and the preimage of a given element in the codomain.
The one-to-one and onto properties are introduced.
Students will be able to prove that a function is one-to-one or that a function is not one-to-one. Students will also be able to prove that a function is onto or that a function is not onto.
The notion of a one-to-one correspondence and the notion of the inverse function of a given function are introduced.
Students will be able to prove that a function is a one-to-one correspondence. Students will also be able to find the inverse function of a given function.
The notion of the composition of two functions is introduced.
Students will be able to find the composition of two functions.
In this lecture, we apply functions to the task of measuring the sizes of sets.
Students will be able to show that two sets have the same cardinality.
The notion of a countable set is introduced. An example of an uncountable set is discussed.
Students will be able to show that a set is countable or that a set is uncountable.
In this lecture, an additional example of an uncountable set is discussed. The Cantor diagonalization process is also introduced.
Students will be able to apply the Cantor diagonalization process to show that a set is uncountable.
The notion of a relation is introduced.
Students will understand what the domain and codomain of a relation are, and students will understand what it means for x to be related to y.
We explore additional examples of relations. The notion of a relation on a set A is introduced. Also, the notion of congruence modulo 5 is introduced.
In this lecture, we explore relationships between 3 or more things.
Students will see examples of n-ary relations.
The properties of reflexivity, symmetry, and transitivity are introduced.
Students will be able to determine if a given relation satisfies these properties.
We explore the properties of the relation of congruence modulo 5.
Students will further reinforce their understanding of the properties of relations.
The notion of equivalence relation is introduced.
Students will be able to prove that a given relation is an equivalence relation.
The notion of a partition induced by an equivalence relation is introduced. The notion of an equivalence class is also introduced.
Students will be able to find the partition induced by an equivalence relation on a set.
We explore the partition induced by congruence modulo 5 on the set of integers.
The notion of an equivalence relation induced by a partition is introduced.
The notion of a partial order relation is introduced.
Students will understand the properties of a partial order relation and what it means for two elements to be comparable.
We explore the 'prerequisite' relation on a set of math courses.
Students will be able to represent a partially ordered set using a directed graph.
The notion of a Hasse diagram of a partial order relation is introduced. The notions of a maximal and of a minimal element are also introduced.
Students will be able to represent a partially ordered set using a Hasse diagram.
The notion of a topological sorting for a partial order relation is introduced.
In this lecture, we find a topological sorting for the prerequisite relation on a set of math courses.
Students will be able to find a topological sorting for a given partial order relation.
In this lecture, we explore a simple example of an algorithm.
The definition of an algorithm is introduced, and the while loop is introduced. The general form of an algorithm is also explained.
Students will understand while loops and the general form of an algorithm.
The definition of correctness of a while loop is introduced.
Students will understand what it means for a while loop to be correct with respect to its pre-condition and post-condition.
The notion of a loop invariant is introduced, and the Loop Invariant Theorem is introduced.
Students will understand how a loop invariant is used to prove the correctness of a while loop.
We prove the correctness of the division algorithm.
Students will be able to prove the correctness of a given algorithm.
The definition of the efficiency of an algorithm is introduced.
Students will understand what the efficiency of an algorithm means.
We explore the linear search algorithm.
In this lecture, we explore the efficiency of the linear search algorithm. The notions of best-case efficiency and worst-case efficiency are introduced.
Students will be able to measure the efficiency of algorithms.
The notion of the order of a function is introduced.
Students will be able to determine the order of a given function.
We explore the binary search algorithm.
In this lecture, we explore the efficiency of the binary search algorithm.
Students will reinforce their ability to measure the efficiency of algorithms. Students will understand what it means for an algorithm to be more efficient than another algorithm.
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.