Details
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.
Learning Outcomes
Learning Outcomes
Upon successful completion of this course, you will be able to:
Course Requirements
- 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.
In order to take this course, you must:
√ Have access to a computer;
√ Have continuous broadband Internet access;
√ Have the ability/permission to install plug-ins or software (e.g. Adobe Reader or Flash);
√ Have the ability to download and save files and documents to a computer;
√ Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);
√ Have competency in the English language;
√ Have read the Saylor Student Handbook;
√ Have completed the following prerequisite courses from The Core Program of the computer science discipline, including CS101 and/or CS102 for use of functions and procedures, conditional statements, loops, recursion, data types, and evaluation of expressions;
√ Have skills in basic algebra and calculus.
√ Have access to a computer;
√ Have continuous broadband Internet access;
√ Have the ability/permission to install plug-ins or software (e.g. Adobe Reader or Flash);
√ Have the ability to download and save files and documents to a computer;
√ Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);
√ Have competency in the English language;
√ Have read the Saylor Student Handbook;
√ Have completed the following prerequisite courses from The Core Program of the computer science discipline, including CS101 and/or CS102 for use of functions and procedures, conditional statements, loops, recursion, data types, and evaluation of expressions;
√ Have skills in basic algebra and calculus.
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Saylor Academy’s mission is to open education to all.
Saylor Academy’s mission is sustained by the continued evolution of an open educational ecosystem, and we are dedicated partners in this movement. Saylor’s commitment to the open education ecosystem is founded not just on open educational resources and open source learning technologies, but also on open access to credentials, and ongoing open learning opportunities.
Guided by these beliefs, Saylor Academy is currently focused on the following projects:
Open Courses: Maintenance and Learner-Centered Improvements
- A commitment to the OER community means that we’ll continue to replace open access materials with openly licensed ones in an effort to make Saylor courseware as reusable and remixable as possible.
- Open courses require more instructional supports for learners, so our current improvements focus on ensuring better and more frequent opportunities for Saylor students to practice what they’re learning.
Open Credentials: Adding New Opportunities and Bolstering Existing Ones
- We’re working on expanding our suite of Saylor Direct credit recommended exams, and we’re also keen on working with university partners to develop innovative and flexible partner degree launching and completion programs. ...
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