Course Syllabus

Learn discrete mathematics in a way that combines theory with practicality. Major topics include single-membership sets, mathematical logic, induction, proofs, counting theory, probability, recursion, graphs, trees, and finite-state machines.

This course includes the following units:

• Unit 1: Sets, Set Relations, and Set Functions
• Unit 2: Counting Theory
• Unit 3: Mathematical Logic
• Unit 4: Mathematical Induction and Proofs
• Unit 5: Probability
• Unit 6: Recursion
• Unit 7: Graphs
• Unit 8: Trees
• Unit 9: Finite-State Automata

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

• Formulate solutions for selected problem classes involving single-membership sets, classifiable situations, or identifiable event categories;
• Apply objective mathematical reasoning to systems composed of discrete objects and events;
• Assess the accuracy of probabilistic statements applied to specific situations;
• Assess mathematical proofs claiming to show whether or not a condition Y holds, given a premise X;
• Interpret situations that have a predetermined sequence of actions that depend on a limited sequence of events;
• Describe sequences of events and mathematical results where the next event or result is a function of previous ones;
• Explain systems of states (collections of variables describing a specific reality) that have an initial state (given values for each variable) and conditions for transitioning (changing values) from one state to another;
• Categorize all possible outcomes for a series of events, or all possible collections of a set of objects;
• Diagram hierarchical relationships between individual entities within a given situation; and
• Apply networks of mathematical or system entities as tools in computer science to solve various real-world problems.

Throughout this course, you will also see learning outcomes in each unit. You can use those learning outcomes to help organize your studies and gauge your progress.

This course's primary learning materials are articles, lectures, and videos.

All course materials are free to access and can be found in each unit of the course. Pay close attention to the notes that accompany these course materials, as they will tell you what to focus on in each resource and will help you understand how the learning materials fit into the course as a whole. You can also see a list of all the learning materials in this course at this link.

Some parts of this course may have been created or reviewed with the support of artificial intelligence (AI). To make sure you receive accurate, high-quality, and academically sound learning materials, all AI-assisted content is carefully checked and approved by Saylor Academy's faculty and subject matter experts.

Only the final exam is considered when awarding you a grade for this course. To pass this course, you will need to earn a grade of 70% or higher on the final exam.

Your score on the exam will be calculated as soon as you complete it. Be sure to study in between each attempt! If you do not pass the exam, you will not complete this course or receive a certificate of completion. You can attempt the exam as many times as you want.

There are end-of-unit assessments in this course that are designed to help you study and do not factor into your final course grade. You can take them as many times as you want until you understand the concepts they cover.

You can see all of these assessments at this link.

The certificate earned by passing this self-paced course displays the program hours you completed and continuing education credits (CEUs). CEUs document successful completion of courses that are designed to improve the knowledge and skills of working adults. Many industries value CEUs, and now your certificate reflects them clearly, and they may be used to support career advancement or to meet professional licensing standards. This course contains 4.4 CEUs.

CS202: Discrete Structures is a self-paced course, meaning you can decide when to start and complete the course. We estimate the "average" student will take hours to complete. We recommend studying at a comfortable pace and scheduling your study time in advance.

Learning new material can be challenging, so here are a few study strategies to help you succeed:

• Take notes on terms, practices, and theories. This helps you understand each concept in context and provides a refresher for later study.
• Test yourself on what you remember and how well you understand the concepts. Reflecting on what you've learned improves long-term memory retention.

This course is delivered entirely online. You will need access to a computer or web-capable mobile device and consistent internet access to view or download resources and complete auto-graded assessments and the final exam.

To access the full course, including assessments and the final exam, log into your Saylor Academy account and enroll in the course. If you don't have an account, you can create one for free here. Note that tracking progress and taking assessments require you to log in.

For more details and guidance, please review our complete Technical Requirements and our student Help Center.

Optional Saylor Academy Mobile App

You can access all course features directly from your mobile browser, but if you have limited internet connectivity, the Saylor Academy mobile app provides an option to download course content for offline use. The app is available for iOS and Android devices.

This course is entirely free to enroll in and access. All course materials, including textbooks, videos, webpages, and activities, are available at no charge. This course also contains a free final exam and a free course completion certificate.