Keywords: Divisibility (8)

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Discrete Structures
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Discrete Structures

This course describes discrete mathematics, which involves processes that consist of sequences ... (more)

This course describes discrete mathematics, which involves processes that consist of sequences 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. Upon successful completion of this course, the student will be able to: 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 or 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 automata; 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, make decisions or select from alternative choices to calculate probabilities, to document derivation steps, or to solve problems; Construct and analyze finite state automata, formal languages, and regular expressions. (Computer Science 202) (less)

Subject:
Science and Technology
Material Type:
Assessments
Full Course
Homework and Assignments
Lecture Notes
Readings
Syllabi
Video Lectures
Provider:
The Saylor Foundation
Provider Set:
Saylor Foundation
Factors and Multiples Puzzle
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Factors and Multiples Puzzle

This puzzle, played with cards on a board (downloadable file), provides an ... (more)

This puzzle, played with cards on a board (downloadable file), provides an interesting context in which students can apply their knowledge of number properties. Students attempt to arrange 25 numbers and 10 property headings into a 5 by 5 grid so that each number satisfies two conditions. Properties addressed include primes, square and triangular numbers, specific sets of multiples and factors, and parity. It can be worked individually or in small groups cooperatively. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to an article, "Using Games in the Classroom" (catalogued separately). (less)

Subject:
Mathematics
Chemistry
Engineering
Life Science
Social Sciences
Education
Material Type:
Activities and Labs
Games
Instructional Material
Provider:
Maryland Public Television
Science and Math Informal Learning Educators (SMILE)
Provider Set:
Mathlanding: Elementary Mathematics Pathway
SMILE Pathway: Science and Math Activities in One Search
Author:
NRICH
Guesswork
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Guesswork

In this activity, students explore number decomposition and the powers of two. ... (more)

In this activity, students explore number decomposition and the powers of two. They play a number guessing game, and by the presence or absence of the secret number on each of six cards, the number can be found. An applet has the computer play the trick with the learner. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for support and extension. (less)

Subject:
Mathematics
Chemistry
Computing and Information
Engineering
Life Science
Social Sciences
Education
Material Type:
Activities and Labs
Games
Instructional Material
Interactive
Provider:
Maryland Public Television
Science and Math Informal Learning Educators (SMILE)
Provider Set:
Mathlanding: Elementary Mathematics Pathway
SMILE Pathway: Science and Math Activities in One Search
Author:
NRICH
Theory of Numbers, Spring 2012
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Theory of Numbers, Spring 2012

This course is an elementary introduction to number theory with no algebraic ... (more)

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.    (less)

Subject:
Mathematics and Statistics
Material Type:
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Abhinav Kumar
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.desu si egaugnal gnimmargorp avaJ ehT .gninnalp dna ,tnemeganam ,ecneics ,gnireenigne ni ... (more)

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