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Gavin Walton
- August 17, 2024
Welcome to the world of ” study.com Math 108 : Discrete Mathematics”! This course is for those who have ever had a curiosity about how mathematicians approach problems or how problems in mathematics/logic are formulated and solved. Discrete Mathematics can be defined as a subject that focuses on difference and Division, therefore it majors on discrete values such as integer values, diagrammatic click-on values, and logical statements. In this course, you will find out how proofs work, topics concerning sets and functions, probability, graph theory, matrices, and Boolean algebra. In fact, it is like getting to know the password that runs the basic acts of human life as well as the higher computer applications.
This course could be viewed as a tool chest for logical and mathematical thinking. If you are looking forward to having a firm grounding in computer science, and data analysis or just want better problem-solving skills, study.com Math 108: Discrete Mathematics is here to make all these concepts easier and fun. Take your seat and be prepared to enter a world that is far from simple counting and arithmetic, which is primarily about figures, connections, and reason. So, my friend, let us proceed with the discovery of this course as well as of discrete mathematics as a subject and I’ll ensure that it’s not only comprehensible but also fun!
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The study.com Math 108 Experience📖
Starting on “study.com Math 108: Discrete Mathematics” means entering a new world while the chapters are the discoveries of a new world in mathematics. Here’s a sneak peek into what you’ll be exploring and mastering:
Logic and Proofs: This is the summed-up essence where everything starts. The understanding of this topic is important because logic is the foundation of all mathematics. Here, you will get information about how to build and break arguments, signs of logical fallacies, and a truth table. You would always expect to find questions on the logical operators, truth values, and if-then statements on the exams.
Sets and Functions: Sets are the basic tools in the kit for working with discrete mathematics. Here you will look at the server concepts like unions, intersections, subsets, as well as cardinality. As for specific topics, the role of sets will be explained in detail, with functions, these objects that map elements belonging to one set to another, receiving particular attention. Basic concepts are tested in this section often so if you get a good grasp of things here then you will reap big later.
Counting Rules, Combinations, and Permutations: Have you ever thought about what is the number of permutations of elements’ sets? This section has it all, the answers are found here. It is for this reason that you will study elements such as counting principle, permutation, and combinations basics to define probability and stats. The next wonderful concept that is called ‘the pigeonhole principle’ will explain to you that it is impossible to put 11 pigeons into 10 pigeonholes without one or more of them having to share a hole.
To achieve success in the course you will be exposed to numerous subjects like graphing theory, recursion, matrices, Boolean algebra, and so on. All of these topics are not only tightly connected with discrete math, but are also widely used in computer science, cryptography, and, of course, networks. One piece of advice is to focus more on the topics such as graph theory and Boolean algebra as these notions are important in the course and are frequently used in the final proctored exam.
At the completion of this course, discrete mathematics will be well understood by you and you will be in a position to solve the most complicated problems. Please remember that when it comes to these topics, steady learning and application are definitely a rule to follow. Let’s dissect it on a weekly basis on how you can excel in this course moving forward.
A Week-by-Week Approach to Math 108 Exam Prep 📝
As you move through this course titled study.com Math 108: Discrete Mathematics it shall be relevant to have a week-by-week guide that will enable you to guide through this course so as to prepare optimally for the proctored exam at the end of the course. This way each week introduces a group of topics, which will be comprehensively covered by the time students finish the course.
Week 1: Introduction to Logic and Proofs
- Day 1-2: Watch the lessons on critical thinking and logic in mathematics. Practice identifying logical fallacies.
- Day 3-4: Study truth tables, propositions, and conditional statements. Take the quiz to test your understanding.
- Day 5-7: Dive into direct proofs and tautologies. Make sure to complete any practice problems and quizzes.
External Resources:
Week 2: Sets and Functions
- Day 1-2: Learn about mathematical sets, elements, intersections, and unions. Practice problems using sets.
- Day 3-4: Study universal sets, complements, and cardinality. Test yourself with quizzes.
- Day 5-7: Understand functions, injections, surjections, and bijections. Watch related videos for additional examples.
External Resources:
- YouTube: Sets and Functions
- Quizlet: Set Theory Flashcards
Week 3: Sequences, Sums, and Induction
- Day 1-2: Watch lessons on arithmetic and geometric sequences. Practice identifying and classifying sequences.
- Day 3-4: Learn about sigma notation and calculating series. Take quizzes to reinforce your knowledge.
- Day 5-7: Study mathematical induction and practice proof techniques. Complete the chapter test.
External Resources:
Week 4: Counting Rules, Combinations, and Permutations
- Day 1-2: Explore the fundamental counting principle and permutations. Solve practice problems.
- Day 3-4: Study combinations and the pigeonhole principle. Test yourself with quizzes.
- Day 5-7: Review and practice the probability of permutations and combinations. Complete the chapter test.
External Resources:
- YouTube: Permutations and Combinations
- Quizlet: Counting Principles Flashcards
Week 5: Discrete Probability
- Day 1-2: Learn about random variables and expected values. Watch related videos for a deeper understanding.
- Day 3-4: Study discrete probability distributions and empirical probability. Take the quiz to check your progress.
- Day 5-7: Review binomial experiments and distributions. Practice problems and complete the chapter test.
External Resources:
Week 6: Binomial Probability
- Day 1-2: Understand binomial experiments and probability formulas. Solve practice problems.
- Day 3-4: Study binomial distribution tables and random variables. Take quizzes to reinforce learning.
- Day 5-7: Review solving problems with binomial experiments. Complete the chapter test.
External Resources:
- YouTube: Binomial Probability
- Quizlet: Binomial Probability Flashcards
Week 7: Recursion and Advanced Counting
- Day 1-2: Learn about recursive functions and recurrence relations. Practice identifying these problems.
- Day 3-4: Study divide-and-conquer algorithms and generating functions. Take quizzes to test your knowledge.
- Day 5-7: Review the inclusion-exclusion principle. Solve practice problems and complete the chapter test.
External Resources:
- YouTube: Recursion in Math
- Quizlet: Recursion Flashcards
Week 8: Graph Theory and Trees
- Day 1-2: Explore graphs, Euler and Hamilton circuits. Solve related practice problems.
- Day 3-4: Study trees, spanning trees, and minimum spanning trees. Take quizzes to reinforce your knowledge.
- Day 5-7: Review traversal methods and applications of trees in discrete mathematics. Complete the chapter test.
External Resources:
Week 9: Matrices in Discrete Math
- Day 1-2: Understand matrices, their properties, and basic operations. Watch videos to supplement your learning.
- Day 3-4: Study inverse matrices and their applications. Solve practice problems.
- Day 5-7: Review matrix rotations and translations. Complete the chapter test.
External Resources:
Week 10: Boolean Algebra and Logic Gates
- Day 1-2: Learn about Boolean logic, operators, and algebra. Practice simplifying Boolean expressions.
- Day 3-4: Study Karnaugh maps and logic gates. Solve related practice problems.
- Day 5-7: Review designing logic circuits and applications of Boolean algebra. Complete the chapter test.
External Resources:
- YouTube: Boolean Algebra
- Quizlet: Boolean Logic Flashcards
Week 11: Review and Practice Tests
- Day 1-2: Review all key concepts from each chapter. Focus on areas where you feel less confident.
- Day 3-4: Take practice tests and quizzes to simulate exam conditions. Identify and work on weak spots.
- Day 5-7: Final review of all topics. Ensure you understand the main concepts and formulas.
External Resources:
- Study.com Practice Tests
- YouTube: Final Exam Review
With the help of this planned schedule, you’ll be ready and prepared to complete the “study. com Math 108: Discrete Mathematics” final proctored exam. Happy studying!
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Math 108: Where to Find Free Study Resources📂
When you are studying for study.com Math 108: Discrete Mathematics: you might come across concepts that are hard to understand at your first glance. So below we have listed several free extra resources that you can peruse to gain a better understanding of them and help you better prepare for the challenge ahead.
YouTube Channels:
- Khan Academy: This channel covers a wide range of mathematical topics, including discrete math. The explanations are clear and easy to follow.
- Professor Leonard: Known for his detailed and comprehensive math lectures, this channel can be especially helpful for deeper dives into specific topics.
- Mathispower4u: This channel offers short, focused tutorials on specific problems and concepts, ideal for quick reviews.
Online Study Platforms:
- Quizlet: Flashcards and practice quizzes can be invaluable for memorizing definitions and key concepts.
- Quizlet Discrete Mathematics Flashcards
- OpenStax: Provides free, peer-reviewed, openly licensed textbooks that are perfect for additional reading and practice problems.
- OpenStax Discrete Mathematics Textbook
Interactive Learning Tools:
- Desmos: While primarily a graphing calculator, Desmos offers tools that are great for visualizing functions, sequences, and more.
- Desmos Graphing Calculator
- Wolfram Alpha: This computational engine can solve a wide variety of math problems, providing step-by-step solutions.
Free Courseware:
- MIT OpenCourseWare: Offers course materials from MIT’s discrete math classes, including lecture notes, assignments, and exams.
- MIT OpenCourseWare Discrete Mathematics
With these external sources, you can also cement what you have learned and hear or read about it in a different way. Good luck, and happy studying!
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Key Topics to Focus On🔑
Before taking the “study.com Math 108: Discrete Mathematics final exam”, it is useful to look at topics that are regularly included in the exams and are essential to mastering the remaining content of the subject. In this article, we shall attempt to explain four general concepts by doing comparisons and then relating them to real-life scenarios so as to tally with the general perception of digesting information.
Logical Operators and Truth Tables
Concept: Logical operators (AND, OR, NOT) are the backbone of mathematical logic and are used to build truth tables, which display the output of logical expressions based on all possible input combinations.
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Operator
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Symbol
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Example
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Result
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AND
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∧
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T ∧ F
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False
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OR
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∨
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T ∨ F
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True
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NOT
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¬
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¬T
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False
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Real-World Example: Think of a simple security system. The alarm will only go off (True) if the motion sensor is triggered (True) AND the window sensor is triggered (True). If either one is False, the alarm stays off.
Sets: Unions and Intersections
Concept: Sets are collections of distinct objects. The union of two sets includes all elements from both sets, while the intersection includes only the elements common to both.
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Operator
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Symbol
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Definition
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Example
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|---|---|---|---|
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Union
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∪
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All elements from both sets
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{1,2} ∪ {2,3} = {1,2,3}
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Intersection
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∩
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Common elements between sets
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{1,2} ∩ {2,3} = {2}
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Real-World Example: Imagine two circles in a Venn diagram representing students who play soccer and students who play basketball. The union represents all students who play either sport, while the intersection represents students who play both sports.
Permutations vs. Combinations
Concept: Permutations and combinations both deal with selecting items from a set. Permutations consider order, while combinations do not.
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Type
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Formula
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Order Matters
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Example
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Permutation
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nPr = n!/(n-r)!
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Yes
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Arranging 3 books on a shelf
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Combination
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nCr = n!/(r!(n-r)!)
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No
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Choosing 3 toppings for a pizza
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Real-World Example: If you’re organizing books (permutations), the order matters. But if you’re choosing toppings for a pizza (combinations), the order doesn’t matter; pepperoni and mushrooms are the same as mushrooms and pepperoni.
Graph Theory: Euler and Hamilton Circuits
Concept: Graph theory studies points (vertices) connected by lines (edges). Euler circuits visit every edge exactly once, while Hamilton circuits visit every vertex exactly once.
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Type
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Definition
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Example
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|---|---|---|
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Euler Circuit
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Visits every edge once
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Inspecting each bridge in a network
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Hamilton Circuit
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Visits every vertex once
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Planning a sales route to each city
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Real-World Example: An example of the Euler circuit problem can be the ‘Seven Bridges of Konigsberg’ whereas the creation of a route that will pass through all cities only once is an example of the Hamilton circuit problem.
So, realizing the meanings of these terms and their practical use will provide you with a firm initial basis for the solution of rather difficult problems on your discrete mathematics exam. Alright, here are some of the most common questions (and answers) that you may have if there were any confusion!
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Math 108: All Your Questions Answered❓
Q: How crucial are quizzes in this course?
A: The quizzes are very essential and significant because they account for a large portion of your total score. They are expected to check your understanding of each topic and also discover the areas that you require more study. Ensure that one gets to maximize the use of the three tries that one is allowed regarding each quiz for a better score.
Q: Is it allowed to take a calculator in the final examination?
A: Yes, it is allowed to bring a non-graphing, scientific calculator during the proctored final exam. Study. com lets you use the Desmos scientific calculator in the exam, so you have no need to bring it yourself.
Q: What should I do if I fail in the final examination the first time?
A: If you failed the final exam the first time around, it is not a big deal. You can take it again within the 3-day waiting period if you do not pass it. Take this opportunity to go over subjects that may have proven hard for you, complete more mock exams, and be sure that you are ready. Just keep in mind every exam taker can take it twice only, so make it as productive as possible.
Q: Does the teaching of this course have any prerequisites?
A: No, there are no prerequisites for “study.com Math 108: Discrete Mathematics.” This course is designed to be accessible to all students, regardless of their prior mathematical background. However, having a basic understanding of algebra and logical reasoning will be beneficial.
Q: How are the things that will be taught to us in this course relevant to real-life scenarios?
A: Discrete mathematics is widely used in practice with an emphasis on such areas as computer science, cryptography, networks, and operations research. Mathematical concepts such as logical reasoning, set theory, graph theory, Boolean algebra, and a host of others are invaluable resources in problem-solving for instance in OPTIMIZING the network paths, designing algorithms in programs, and many others.
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Conclusion of Math 108📄
Well done for embarking on the first part of this instructional program on “study.com Math 108: Discrete Mathematics”. This course provides simple, clear, and interesting insights into a number of mathematical concepts that are both entertaining and fully applicable in everyday life. Thus, by keeping to the study schedule, using sources outside this material, and concentrating on the identified key issues, you will be ready for the final exam.
Remember, consistency is key. Stay consistent with your studying and practicing and do not be embarrassed to ask for help if you need it. So I thought, with proper commitment, specifically towards learning discrete mathematics, and having the right approach towards it, one will realize that it is as easy and as fun as one can make it. Have good luck, follow your dreams, and enjoy studying! You’ve got this!
