Discrete mathematics is foundational material for computer science: Many areas of computer science require the ability to work with concepts from discrete mathematics, specifically material from such areas as set theory, logic, graph theory, combinatorics, and probability theory.
The material in discrete mathematics is pervasive in the areas of data structures and algorithms but appears elsewhere in computer science as well. For example, an ability to create and understand a proof is important in virtually every area of computer science, including (to name just a few) formal specification, verification, databases, and cryptography. Graph theory concepts are used in networks, operating systems, and compilers. Set theory concepts are used in software engineering and in databases. Probability theory is used in artificial intelligence, machine learning, networking, and a number of computing applications.
Discrete Mathematics Syllabus Pdf Download
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Note that this document is intended to be a high-level guide to the types of concepts and level of understanding expected for passing the Discrete Mathematics proficiency exam. It should not be taken as an exhaustive list of material that might appear on the exam. Students should be comfortable solving problems in the areas described in this document. These topics map roughly to the following sections of the text Discrete Mathematics with Graph Theory, Third Edition, by Goodaire and Parmenter, copies of which can be found on reserve at the Schow library.
This course is a one-semester introduction to discrete mathematics with an emphasis on the understanding, composition and critiquing of mathematical proofs. At the semester's conclusion, the successful student will be able to:
Discrete mathematics is not coordinated in the same sense as other multi-section courses with a common final exam (e.g., calculus). As such the instructor has final discretion in topics chosen and course policies. Below are syllabi from recent implementations.
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Topics chosen from discrete mathematics. May include counting and probability, sequences, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems, voting methods, apportionment methods, mathematics of finance, number theory.
Linear equations and inequalities, matrices, systems of linear equations, and linear programming; sets, counting, probability and statistics; mathematics of finance; applications to business and economics.
Limits, continuity, differentiation, antidifferentiation, definite integral, with applications to the physical sciences and engineering sciences. Suitable for students with some prior calculus experience. Substitutes for MATH 1151 as a requirement.
Transcendental functions, formal integration, polar coordinates, infinite sequences and series, vector algebra and geometry, with applications to the physical sciences and engineering. Substitutes for MATH 1122 as a requirement.
Interviews will be conducted before certification is granted. The Math Department will not certify candidates that have earned a degree completely through online coursework or who do not have a degree in an appropriate field.
MATH 2110Q To be eligible for certification in MATH 2110Q, instructors must first meet requirements to teach MATH 1131Q and 1132Q (possess a strong background as a math major and have a grade of at least a B in a Real Analysis I course). Instructors seeking to be certified in MATH 2110Q in addition to MATH 1131Q and 1132Q should have successfully taught each course at least twice. Additionally, to be certified to teach MATH 2110Q, instructors should possess a very strong background as a math major and have successfully completed at least four upper-level, proof-based courses (Real Analysis I & II, Abstract Algebra I & II, Abstract Linear Algebra, Complex Analysis, Differential Geometry, Number Theory, etc.) with a grade of a B or higher in each course. Exceptions may be made in extenuating circumstances at the discretion of the faculty coordinator.
Discrete Mathematics deals with the study of Mathematical structures. It deals with objects that can have distinct separate values. It is also called Decision Mathematics or finite Mathematics. It is the study of mathematical structures that are fundamentally discrete in nature and it does not require the notion of continuity.
Objects that are studied in discrete mathematics are largely countable sets such as formal languages, integers, finite graphs, and so on. Due to its application in Computer Science, it has become popular in recent decades. It is used in programming languages, software development, cryptography, algorithms etc. Discrete Mathematics covers some important concepts such as set theory, graph theory, logic, permutation and combination as well. In this article, let us discuss these important concepts in detail.
Set Theory: Set theory is defined as the study of sets which are a collection of objects arranged in a group. The set of numbers or objects can be denoted by the braces {} symbol. For example, the set of first 4 even numbers is {2,4,6,8}
Graph Theory: It is the study of the graph. The graph is a mathematical structure used to pair the relation between objects. Graphs are one of the prime objects of study in Discrete Mathematics.
Sequence: According to some definite rules, a set of numbers arranged in a definite order is called a Sequence. A sequence is a function whose domain is the countable set of natural numbers.
Part of the reason discrete mathematics is difficult is that it has a significantly different flavor than the mathematics classes you have taken prior to this course. Unlike college algebra, learning about the concepts and point of view of discrete mathematics is at least as important as mastering various computational techniques.
The methods used to describe and solve problems in discrete mathematics are as varied as the topics. You will learn about permutations, combinations, inclusion-exclusion counting, characteristic polynomials for recurrences, rules of logical and methods of doing proofs, and properties of sets, and other tidbits along the way.
Besides vocabulary and methods, another central goal of discrete mathematics is learning to read and construct proofs, particularly writing proofs using the method of induction. Induction is certainly one of the basic tools of both computer science and mathematics. You might find learning to read and do proofs will be the greatest challenge in this online course.
This course has 18 online lessons and 3 proctored exams, proctored by ProctorU Live+. You can submit up to 3 items per week, taking as little as 7 weeks and a maximum of 9 months to complete the course. Allow an additional 7-10 business days to process registration, and 3-5 days for the final grade to appear on your transcript.
You may enroll at any time and have up to 9 months to complete this online course. The credits earned will be recorded on your UND transcript based on the date you registered for the course. It will appear on your transcript in the same way as a course taken during a regular semester. There is no indication that the course was taken online or that you completed it at your own pace.
During my sophomore year at Dartmouth I took a course in discrete mathematics. The tests were not calibrated to any standard scale, so it was difficult to judge how well you were doing. On the midterm, for example, scores around 50 to 60 out of 100 were at the top of the class, whereas for the final those would be failing.
This was hard to believe. The course had 70 students. Three of them were from Eastern Europe where, educated in the old Soviet-style talent-tracking system, they had already studied this subject in high school!
At the high-level, my strategy was exactly what I spelled out in my How to Ace Calculus post of two weeks ago: learn the insights. But I want to dive into the details of how I accomplished this goal for this specific class. Think of this as a case study of the insight method in action.
I think you missed completely point of the article. He was not just re-copying his notes, he was going through every proof from scratch and making sure he got it right and understood every step. That is a far cry from just re-copying notes.
That is the opposite of the insight of this post. I taught myself to be able to recreate every proof taught in the course from scratch. Building the study guides was just the setup phase for the insight-driven review that followed.
Hmm..
I also do something like that at math. Just review ALL the questions asked in the book. And in the period, I make ALL the questions, not the one the teacher gives to us, but all of them.
It works.
Thanks Cal! This method helped me do well in Organic Chem, where the professor would write examples on the board, but take less than straight forward routes to solve them. By writing each type of problem on a paper, and practicing them until I could do them with no hesitation or problem, I was able to do well on his tests.
I found that a technique similar to this worked in my climatology course this term. We needed to be able to use the locations of semi-permanent features (meteorologically) and how they interact to create specific climates. I constantly was printing copies of maps and writing in the features to create a study guide for each season. It might not be writing proofs, but making sure you know how things work is a key part of any natural or applied science course.
I used that technique for my molecular bio class. I was able to recreate every lecture and detail in my notes, and I studied with my friend who crammed. Before each exam, I was teaching the material to him because I knew it so well. I just got one of the highest grades in the entire class and got the single highest score on the second exam. 152ee80cbc
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