Specific information about this course and its requirements can be found below. For more general information about taking Saylor Academy courses, including information about Community and Academic Codes of Conduct, please read the Saylor Student Handbook.

Introduction to the mathematical foundations from discrete mathematics for analyzing computer algorithms, both for correctness and performance. Focuses on the introduction to models of computation, including finite state machines and Turing machines.

This course has been designed to provide you with a clear, accessible introduction to discrete mathematics. Discrete mathematics describes processes that consist of a sequence of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. As you progress through the units of this course, you will develop the mathematical foundations necessary for more specialized subjects in computer science, including data structures, algorithms, and compiler design. Upon completion of this course, you will have the mathematical know-how required for an in-depth study of the science and technology of the computer age.

**This course is comprised of the following units:**

- Unit 1: The Logic of Compound Statements
- Unit 2: The Logic of Quantified Statements
- Unit 3: Introduction to Number Theory and Proof Methods
- Unit 4: Mathematical Induction and Introduction to Sequences
- Unit 5: Set Theory
- Unit 6: Introduction to Counting and Probability
- Unit 7: Recursion
- Unit 8: Graphs and Trees
- Unit 9: Regular Expressions and Finite-State Automata

Upon successful completion of this course, you will be able to:

- create compound statements, expressed in mathematical symbols or in English, to determine the truth or falseness of compound statements and to use the rules of inference to prove a conclusion statement from hypothesis statements by applying the rules of propositional and predicate calculus logic;
- prove mathematical statements involving numbers by applying various proof methods, which are based on the rules of inference from logic;
- prove the validity of sequences and series and the correctness of repeated processes by applying mathematical induction;
- define and identify the terms, rules, and properties of set theory and use these as tools to support problem solving and reasoning in applications of logic, functions, number theory, sequences, counting, probability, trees and graphs, and finite state machines;
- calculate probabilities and apply counting rules;
- solve recursive problems by applying knowledge of recursive sequences;
- create graphs and trees to represent and help prove or disprove statements, to make decisions or select from alternative choices, to calculate probabilities, to document derivation steps, or to solve problems; and
- construct and analyze finite state automata (another name for machines), formal languages, and regular expressions.

The primary learning materials for this course are readings, lectures, video tutorials, and other resources.

All course materials are free to access, and can be found through the links provided in each unit and subunit of the course. Pay close attention to the notes that accompany these course materials, as they will instruct you as to what specifically to read or watch at a given point in the course, and help you to understand how these individual materials fit into the course as a whole. You can also access a list all of the materials used in this course by clicking on Resources in the course's "Activities" menu.

**Only the final exam is considered when awarding you a grade for this course**. In order to pass this course, **you will need to earn a 70% or higher on the final exam**. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam on your first attempt, you may take it again as many times as needed, following a 7-day waiting period between each attempt. Once you have successfully passed the final exam you will be awarded a free Saylor Certificate of Completion.

There are also **8 unit assessments and other types of quizzes** in this course. These are intended to help you to gauge how well you are learning and **do not factor into your final course grade**. You may retake all of these as many times as needed to feel that you have an understanding of the concepts and material covered. You can locate a full list of these sorts of assessments by clicking on Quizzes in the course's "Activities" menu.

This course provides students the opportunity to earn actual college credit. It has been reviewed by **Brandman University** and can applied as credit towards a degree by students who are currently enrolled or plan to enroll at Brandman. You can read more about this special program here.

**If you are seeking to earn college credit at Brandman, you must take and pass the version of the exam titled "Proctored Final Exam." That exam will be password protected.**

**Note**: There is a 14-day waiting period between attempts of the Direct Credit final exam. There is no imposed wait period between attempting the non-credit certificate-bearing exam and the credit exam. Some credit exams have a maximum number of attempts allowed, which will be detailed on the exam's instructions page.

CS202: Discrete Structures is a **self-paced course** in which you the learner determines when you will start and when you will complete the course. There is no instructor or predetermined schedule to follow. While learning styles can vary considerably and any particular student will take more or less time to learn or read, we estimate that the "average" student will take **106 hours** to complete this course. We recommend that you work through the course at a pace that is comfortable for you and allows you to make regular (daily, or at least weekly) progress. It's a good idea to also schedule your study time in advance and try as best as you can to stick to that schedule.

Learning new material can be challenging, so below we've compiled a few suggested study strategies to help you succeed:

- Take notes on the various terms, practices, and theories as you read. This can help you differentiate and contextualize concepts and later provide you with a refresher as you study.
- As you progress through the materials, take time to test yourself on what you have retained and how well you understand the concepts. The process of reflection is important for creating a memory of the materials you learn; it will increase the probability that you ultimately retain the information.
- Although you may work through this course completely independently, you may find it helpful to connect with other Saylor Academy students through the discussion forums. You may access the discussion forums at https://discourse.saylor.org.

In order to take this course you should:

This course is delivered fully online. You will be required to have access to a computer or web-capable mobile device and have consistent access to the internet to either view or download the necessary course resources and to attempt any auto-graded course assessments and the final exam.

- To access the full course including assessments and the final exam, you will need to be logged into your
**Saylor Academy account**and enrolled in the course. If you do not already have an account, you may create one, free of charge, here. Although you can access some course resources without being logged into your account, it's advised that you log in to maximize your course experience. For example, some of the accessibility and progress tracking features are only available when you are logged in. - If you plan to attempt the optional credit recommended final exam that accompanies this course, then you will also
**need access to a webcam enabled computer**. A webcam is needed so that our remote proctoring service can verify your identity, which will allow Saylor Academy to issue an official transcript to schools on your behalf.

For additional technical guidance check out Saylor Academy's tech-FAQ and the Moodle LMS tutorial.

**There is no cost to access and enroll in this course**. All required course resources linked throughout the course, including textbooks, videos, webpages, activities, etc are accessible for no charge. This course also contains a free final exam and course completion certificate.

This course does contain an optional final exam that will provide students an opportunity to earn college credit. Access to the exam itself is free, though it does require the use of a proctoring service for identity verification purposes. **The cost for proctoring is $25 per session.**

Last modified: Wednesday, October 2, 2019, 12:35 PM