Discrete Structures  (Mathematics Code)
Discrete Structures  (Mathematics Code) Syllabus

Course Code: Math 340 (math code)
Transcript:
Yes. Your transcript will come from the records office at United States University. They are regionally accredited and award semester credits.
Credits: 4 Semester
Transfer: 4 year degree applicable
Your college will require any class you wish to transfer to them to be from a regionally accredited college that awards academic semester or quarter credits.They will also want the course description of the course to match their own. United States University is regionally accredited and issues academic semester credits. Our course description will match or exceed your college's description; thus, your college will most likely accept the course and apply it towards your degree. If you would like preapproval from your school, please send your counselor or registrar's office the link at the bottom of this page.Your college may be one of the many schools that we are associated with, so check the Associated School link before asking for preapproval. (K12 use)
Enrollment Schedule:
Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the selfpaced courses as soon as they are able. Most students finish the lower level courses in 4  8 weeks. The upper level math classes, such as Calculus and above, usually take students 34 months. (Note: The 30day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)
Required Textbook:
No outside textbook is needed. Our Omega Math^{TM} courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.
Grading Mode:
Standard Letter Grade
Proctored Final: Yes
Description
This course was designed for students in math and computer science. Logic is emphasized in this course, and topics include proof and theory (including inductive and deductive proofs), propositional and predicate logic, set theory, algorithms (including recursion), trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs (including Dijkstra's shortest path algorithm). Additionally, an introduction to complexity of algorithms and recurrence relations are included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.
Prerequisite: College Algebra or Precalculus with a grade of C or better.Learning Outcomes
Upon successful completion of Discrete Structures, a student should be able to:
 Effectively express themselves in a precise written form.
 Demonstrate the ability to think critically and logically.
 Students should be able to distinguish between a definition and a theorem, and apply them correctly.
 Read, comprehend and construct mathematical arguments.
 Construct standard proofs, using direct, contradiction, contrapositive, if and only if and inductive arguments.
 Demonstrate the ability to integrate knowledge and ideas in a coherent and meaningful manner.
 Represent discrete objects using the abstract mathematical structures such as sets, permutations, relations, functions, trees and graphs.
 Demonstrate appropriate techniques for specific problems in graph theory, and be able to develop and apply algorithms to solve these problems.
 Demonstrate competencies, and thought processes in the fundamental concepts of graph theory, set theory, and combinatorics, at a level necessary for more advanced mathematics courses.
 Demonstrate realworld problem solving skills. Analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.
Methods of Evaluation:
Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)Homework Quizzes: 15%
Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your longterm memory, and aids in building abstract thinking.
Chapter Tests: 60%
After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.
Proctored Final: 25%
This course go towards a degree which means it must have a proctored final. Your college is accepting this course because it goes through a regionally accredited university, which tells them the class will have a proctored final, and the 60% rule will apply. Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met.
The final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final
The final exam is a comprehensive final covering all of the chapters of the course. Other than scratch paper, you may view the "Authorized Materials" list for the final exam for each class.
 Students must obtain a 60% or better on the final exam in order to get a C or better in the class.
 Students that obtain a grade of an F on the final can receive at most a D in the class. Students that obtain a D on the final can receive at most a C in the class. Students that obtain a C on the final can receive at most a B in the class.
The 60% rule was set in place to protect the integrity of online math education by requiring a display of competency in exchange for a grade. All schools which are regionally accredited adhere to online standards. Your college is accepting this course because it goes through a regionally accredited university, which tells your college that standards have been met. Your college will not accept a class from a school that is not regionally accredited, because they know the standards won't be met.
Assessment:
A 90100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 8089 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 7079 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 6069 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 059 F Quality and quantity of work is below average and not sufficient to progress.Course Content Menu:
Chapter 1
Logic
Lessons Homework HW Quiz 1.1 Nonlinear Inequalities 1.1 1.1 1.2 Truth Tables & Propositions 1.2 1.2 1.3 Logic Operators 1.3 1.3 1.4 Quantifiers  Part 1 1.4 1.4 1.5 Quantifiers  Part 2 1.5 1.5 Chapter 1 Test  (23 online, 11 essay questions)
Chapter 2
Formal Proofs
Lessons Homework HW Quiz 2.1 Truth Tables 2.1 2.1 2.2 Direct Proof 2.2 2.2 2.3 Proof by Contradiction 2.3 2.3 2.4 Proof by Contrapositive 2.4 2.4 2.5 If and only if Proof 2.5 2.5 2.6 Proof by Induction 2.6 2.6 Chapter 2 Test  (9 online, 8 essay questions)
Chapter 3
Sets and Relations
Lessons Homework HW Quiz 3.1 Introduction to Sets 3.1 3.1 3.2 Venn Diagrams 3.2 3.2 3.3 Relations 3.3 3.3 3.4 Equivalence Relations 3.4 3.4 3.5 Matrices of Relations 3.5 3.5 3.6 Functions 3.6 3.6 3.7 Sequences & Series 3.7 3.7 Chapter 3 Test  (28 online, 13 essay questions)
Chapter 4
Algorithms
Lessons Homework HW Quiz 4.1 Introduction to Algorithms 4.1 4.1 4.2 The Euclidean Algorithm 4.2 4.2 4.3 Recursive Algorithms 4.3 4.3 4.4 Complexity of Algorithms 4.4 4.4 Chapter 4 Test  (18 online, 6 essay questions)
Chapter 5
Graph Theory
Lessons Homework HW Quiz 5.1 Introduction to Graph Theory 5.1 5.1 5.2 Cycle and Paths 5.2 5.2 5.3 Hamiltonian Cycles 5.3 5.3 5.4 Matrices of Relations 5.4 5.4 5.5 Dijkstra's Algorithm 5.5 5.5 5.6 Isomorphic Graphs 5.6 5.6 5.7 Planar Graphs 5.7 5.7 Chapter 5 Test  (27 online, 9 essay questions)
Chapter 6
Trees
Lessons Homework HW Quiz 6.1 Introduction to Trees 6.1 6.1 6.2 Depth First Search Algorithm 6.2 6.2 6.3 Breath First Search Algorithm 6.3 6.3 6.4 Minimal Spanning Trees 6.4 6.4 Chapter 6 Test  (7 online, 6 essay questions)
Chapter 7
Recurrence Relations and FiniteState Machines
Lessons Homework HW Quiz 7.1 Introduction to Recurrence Relations 7.1 7.1 7.2 Solving Recurrence Relations 7.2 7.2 7.3 Introduction to FiniteState Machines 7.3 7.3 Chapter 7 Test  (8 online, 9 essay questions)
Chapter 8
Counting and Probability
Lessons Homework HW Quiz 8.1 Counting 8.1 8.1 8.2 Permutations and Combinations 8.2 8.2 8.3 Finite Basic Probabilities 8.3 8.3 8.4 Basic Probability Laws 8.4 8.4 Chapter 8 Test  (31 online, 0 essay questions)
Final for Discrete Structures  (44 online, 16 essay questions)
Time on Task:
This course is online and your participation at home is imperative. A minimum of 8  10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirtyday extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.
Schedule:
Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.
Week Complete Sections 1 1.1  1.3 2 1.4  1.5 3 2.1  2.2 4 2.3  2.4 5 2.5  2.6 6 3.1  3.2 7 3.3  3.5 8 3.6  3.7 9 4.1  4.3 10 4.4  5.1 11 5.2  5.4 12 5.5  5.6 13 5.7  6.1 14 6.2  6.4 15 7.1  7.3 16 8.1  8.2 17 8.3  8.4 Final Exam Conduct Code:
Code of Ethics:
Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.
Respectful communications:
When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.
We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.
Grading information and proctored final policies:
The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade. By agreeing to the terms of service agreement, you agree to read the 'Grading' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first login to notify us if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies. There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.
Examples of academic misconduct:
Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.
Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.
By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.
Other forms of cheating include receiving or providing unpermitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for regrading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.
Unauthorized collaboration:
Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.
Important Notes:
This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.
 Effectively express themselves in a precise written form.

Course Code: DEV5 E875
Transcript:
Yes, from Cal Poly State University.
Credits: 5 CEU
Transfer:
Enrollment Schedule:
Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the selfpaced courses as soon as they are able. Most students finish the lower level courses in 4  8 weeks. The upper level math classes, such as Calculus and above, usually take students 34 months. (Note: The 30day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)
Required Textbook:
No outside textbook is needed. Our Omega Math^{TM} courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.
Grading Mode:
Standard Letter Grade
Proctored Final: No
Description
This course is designed for students in math and computer science. Logic is emphasized in this course, and topics include: proof and theory including inductive and deductive proofs, propositional and predicate logic and calculus, set theory, algorithms including recursion, trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs including Dijkstra's shortest path algorithm. Additionally, an introduction to complexity of algorithms and recurrence relations is included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.
Prerequisite: College Algebra or Precalculus with a grade of C or better.Learning Outcomes
Upon successful completion of Discrete Structures, a student should be able to:
 Effectively express themselves in a precise written form.
 Demonstrate the ability to think critically and logically.
 Students should be able to distinguish between a definition and a theorem, and apply them correctly.
 Read, comprehend and construct mathematical arguments.
 Construct standard proofs, using direct, contradiction, contrapositive, if and only if and inductive arguments.
 Demonstrate the ability to integrate knowledge and ideas in a coherent and meaningful manner.
 Represent discrete objects using the abstract mathematical structures such as sets, permutations, relations, functions, trees and graphs.
 Demonstrate appropriate techniques for specific problems in graph theory, and be able to develop and apply algorithms to solve these problems.
 Demonstrate competencies, and thought processes in the fundamental concepts of graph theory, set theory, and combinatorics, at a level necessary for more advanced mathematics courses.
 Demonstrate realworld problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.
Methods of Evaluation:
Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)Homework Quizzes: 15%
Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your longterm memory, and aids in building abstract thinking.
Chapter Tests: 60%
After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.
Assessment:
A 90100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 8089 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 7079 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 6069 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 059 F Quality and quantity of work is below average and not sufficient to progress.Course Content Menu:
Chapter 1
Logic
Lessons Homework HW Quiz 1.1 NonLinear Inequalities 1.1 1.1 1.2 Truth Tables & Propositions 1.2 1.2 1.3 Logic Operators 1.3 1.3 1.4 Quantifiers  Part 1 1.4 1.4 1.5 Quantifiers  Part 2 1.5 1.5 Chapter 1 Test  (23 online, 11 essay questions)
Chapter 2
Formal Proofs
Lessons Homework HW Quiz 2.1 Truth Tables 2.1 2.1 2.2 Direct Proof 2.2 2.2 2.3 Proof by Contradiction 2.3 2.3 2.4 Proof by Contrapositive 2.4 2.4 2.5 If and only if Proof 2.5 2.5 2.6 Proof by Induction 2.6 2.6 Chapter 2 Test  (9 online, 8 essay questions)
Chapter 3
Sets and Relations
Lessons Homework HW Quiz 3.1 Introduction to Sets 3.1 3.1 3.2 Venn Diagrams 3.2 3.2 3.3 Relations 3.3 3.3 3.4 Equivalence Relations 3.4 3.4 3.5 Matrices of Relations 3.5 3.5 3.6 Functions 3.6 3.6 3.7 Sequences & Series 3.7 3.7 Chapter 3 Test  (28 online, 13 essay questions)
Chapter 4
Algorithms
Lessons Homework HW Quiz 4.1 Introduction to Algorithms 4.1 4.1 4.2 The Euclidean Algorithm 4.2 4.2 4.3 Recursive Algorithms 4.3 4.3 4.4 Complexity of Algorithms 4.4 4.4 Chapter 4 Test  (18 online, 6 essay questions)
Chapter 5
Graph Theory
Lessons Homework HW Quiz 5.1 Introduction to Graph Theory 5.1 5.1 5.2 Cycle and Paths 5.2 5.2 5.3 Hamiltonian Cycles 5.3 5.3 5.4 Matrices of Relations 5.4 5.4 5.5 Dijkstra's Algorithm 5.5 5.5 5.6 Isomorphic Graphs 5.6 5.6 5.7 Planar Graphs 5.7 5.7 Chapter 5 Test  (27 online, 9 essay questions)
Chapter 6
Trees
Lessons Homework HW Quiz 6.1 Introduction to Trees 6.1 6.1 6.2 Depth First Search Algorithm 6.2 6.2 6.3 Breath First Search Algorithm 6.3 6.3 6.4 Minimal Spanning Trees 6.4 6.4 Chapter 6 Test  (7 online, 6 essay questions)
Chapter 7
Recurrence Relations and FiniteState Machines
Lessons Homework HW Quiz 7.1 Introduction to Recurrence Relations 7.1 7.1 7.2 Solving Recurrence Relations 7.2 7.2 7.3 Introduction to FiniteState Machines 7.3 7.3 Chapter 7 Test  (8 online, 9 essay questions)
Chapter 8
Counting and Probability
Lessons Homework HW Quiz 8.1 Counting 8.1 8.1 8.2 Permutations and Combinations 8.2 8.2 8.3 Finite Basic Probabilities 8.3 8.3 8.4 Basic Probability Laws 8.4 8.4 Chapter 8 Test  (31 online, 0 essay questions)
Final for Discrete Structures  (44 online, 16 essay questions)
Time on Task:
This course is online and your participation at home is imperative. A minimum of 13  15 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirtyday extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.
Schedule:
Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.
Week Complete Sections 1 1.1  1.3 2 1.4  1.5 3 2.1  2.2 4 2.3  2.4 5 2.5  2.6 6 3.1  3.2 7 3.3  3.5 8 3.6  3.7 9 4.1  4.3 10 4.4  5.1 11 5.2  5.4 12 5.5  5.6 13 5.7  6.1 14 6.2  6.4 15 7.1  7.3 16 8.1  8.2 17 8.3  8.4 Final Exam Conduct Code:
Code of Ethics:
Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.
Respectful communications:
When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.
We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.
Grading information and proctored final policies:
The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade. By agreeing to the terms of service agreement, you agree to read the 'Grading' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first login to notify us if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies. There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.
Examples of academic misconduct:
Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.
Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.
By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.
Other forms of cheating include receiving or providing unpermitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for regrading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.
Unauthorized collaboration:
Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.
Important Notes:
This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.
 Effectively express themselves in a precise written form.

Course Code: none
Transcript:
A certificate of completion is issued from Omega Math. This course under the noncredit option does not go through one of our partner universities; thus, a transcript is not included with the course.
Credits: 0
Certificate of Completion: Yes
Transfer:
If you would like to take this class for personal enrichment, the noncredit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. If you want to transfer the course to your college, you will need to enroll under the semester credit option. If you would like preapproval from your school, please send your counselor or registrar's office the link to this page. The noncredit courses can also be used to learn the material and then receive credit at a home college using Credit by Examination. (K12 use)
Enrollment Schedule:
Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the selfpaced courses as soon as they are able. Most students finish the lower level courses in 4  8 weeks. The upper level math classes, such as Calculus and above, usually take students 34 months. (Note: The 30day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)
Required Textbook:
No outside textbook is needed. Our Omega Math^{TM} courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.
Grading Mode:
Standard Letter Grade
Proctored Final: No
Description
This course is designed for students in math and computer science. Logic is emphasized in this course, and topics include: proof and theory including inductive and deductive proofs, propositional and predicate logic and calculus, set theory, algorithms including recursion, trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs including Dijkstra's shortest path algorithm. Additionally, an introduction to complexity of algorithms and recurrence relations is included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.
Prerequisite: College Algebra or Precalculus with a grade of C or better.Learning Outcomes
Upon successful completion of Discrete Structures, a student should be able to:
 Effectively express themselves in a precise written form.
 Demonstrate the ability to think critically and logically.
 Students should be able to distinguish between a definition and a theorem, and apply them correctly.
 Read, comprehend and construct mathematical arguments.
 Construct standard proofs, using direct, contradiction, contrapositive, if and only if and inductive arguments.
 Demonstrate the ability to integrate knowledge and ideas in a coherent and meaningful manner.
 Represent discrete objects using the abstract mathematical structures such as sets, permutations, relations, functions, trees and graphs.
 Demonstrate appropriate techniques for specific problems in graph theory, and be able to develop and apply algorithms to solve these problems.
 Demonstrate competencies, and thought processes in the fundamental concepts of graph theory, set theory, and combinatorics, at a level necessary for more advanced mathematics courses.
 Demonstrate realworld problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.
Methods of Evaluation:
Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)Homework Quizzes: 15%
Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your longterm memory, and aids in building abstract thinking.
Chapter Tests: 60%
After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.
Assessment:
A 90100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 8089 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 7079 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 6069 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 059 F Quality and quantity of work is below average and not sufficient to progress.Course Content Menu:
Chapter 1
Logic
Lessons Homework HW Quiz 1.1 NonLinear Inequalities 1.1 1.1 1.2 Truth Tables & Propositions 1.2 1.2 1.3 Logic Operators 1.3 1.3 1.4 Quantifiers  Part 1 1.4 1.4 1.5 Quantifiers  Part 2 1.5 1.5 Chapter 1 Test  (23 online, 11 essay questions)
Chapter 2
Formal Proofs
Lessons Homework HW Quiz 2.1 Truth Tables 2.1 2.1 2.2 Direct Proof 2.2 2.2 2.3 Proof by Contradiction 2.3 2.3 2.4 Proof by Contrapositive 2.4 2.4 2.5 If and only if Proof 2.5 2.5 2.6 Proof by Induction 2.6 2.6 Chapter 2 Test  (9 online, 8 essay questions)
Chapter 3
Sets and Relations
Lessons Homework HW Quiz 3.1 Introduction to Sets 3.1 3.1 3.2 Venn Diagrams 3.2 3.2 3.3 Relations 3.3 3.3 3.4 Equivalence Relations 3.4 3.4 3.5 Matrices of Relations 3.5 3.5 3.6 Functions 3.6 3.6 3.7 Sequences & Series 3.7 3.7 Chapter 3 Test  (28 online, 13 essay questions)
Chapter 4
Algorithms
Lessons Homework HW Quiz 4.1 Introduction to Algorithms 4.1 4.1 4.2 The Euclidean Algorithm 4.2 4.2 4.3 Recursive Algorithms 4.3 4.3 4.4 Complexity of Algorithms 4.4 4.4 Chapter 4 Test  (18 online, 6 essay questions)
Chapter 5
Graph Theory
Lessons Homework HW Quiz 5.1 Introduction to Graph Theory 5.1 5.1 5.2 Cycle and Paths 5.2 5.2 5.3 Hamiltonian Cycles 5.3 5.3 5.4 Matrices of Relations 5.4 5.4 5.5 Dijkstra's Algorithm 5.5 5.5 5.6 Isomorphic Graphs 5.6 5.6 5.7 Planar Graphs 5.7 5.7 Chapter 5 Test  (27 online, 9 essay questions)
Chapter 6
Trees
Lessons Homework HW Quiz 6.1 Introduction to Trees 6.1 6.1 6.2 Depth First Search Algorithm 6.2 6.2 6.3 Breath First Search Algorithm 6.3 6.3 6.4 Minimal Spanning Trees 6.4 6.4 Chapter 6 Test  (7 online, 6 essay questions)
Chapter 7
Recurrence Relations and FiniteState Machines
Lessons Homework HW Quiz 7.1 Introduction to Recurrence Relations 7.1 7.1 7.2 Solving Recurrence Relations 7.2 7.2 7.3 Introduction to FiniteState Machines 7.3 7.3 Chapter 7 Test  (8 online, 9 essay questions)
Chapter 8
Counting and Probability
Lessons Homework HW Quiz 8.1 Counting 8.1 8.1 8.2 Permutations and Combinations 8.2 8.2 8.3 Finite Basic Probabilities 8.3 8.3 8.4 Basic Probability Laws 8.4 8.4 Chapter 8 Test  (31 online, 0 essay questions)
Final for Discrete Structures  (44 online, 16 essay questions)
Time on Task:
This course is online and your participation at home is imperative. A minimum of 8  10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirtyday extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.
Schedule:
Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.
Week Complete Sections 1 1.1  1.3 2 1.4  1.5 3 2.1  2.2 4 2.3  2.4 5 2.5  2.6 6 3.1  3.2 7 3.3  3.5 8 3.6  3.7 9 4.1  4.3 10 4.4  5.1 11 5.2  5.4 12 5.5  5.6 13 5.7  6.1 14 6.2  6.4 15 7.1  7.3 16 8.1  8.2 17 8.3  8.4 Final Exam Conduct Code:
Code of Ethics:
Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.
Respectful communications:
When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.
We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.
Grading information and proctored final policies:
The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade. By agreeing to the terms of service agreement, you agree to read the 'Grading' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first login to notify us if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies. There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.
Examples of academic misconduct:
Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.
Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.
By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.
Other forms of cheating include receiving or providing unpermitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for regrading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.
Unauthorized collaboration:
Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.
Important Notes:
This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.
 Effectively express themselves in a precise written form.