Logic and Mathematical Proof notes
18 notes by 17 users
This page gathers over 10 community-made notes on logic and mathematical proof, from conditional statements to induction. They offer university students and professional candidates proof methods to practise, school students topics to review, and teachers material to use across school and university levels. Pick a note to start exploring.
Notes
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Chapter 2: If Then Statements and Converses
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MT181
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PROOF Proof by contradiction To prove a statement by contradiction you first assume the statement in the question is false, this will be your assumption. Once you have stated your assumption you will attempt to prove your a...
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Conclusions Reflexive Property- A quantity is equal to itself ( think SHARED) Partition-A whole angle,line segment,etc. is equal to the sum of its parts Addition Postulate-Equals added to equals are congruent (GRAPS OR GAPS)
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Mathematical Proving Strategies - created from Mind Map DIRECT PROOF CONTRAPOSITIVE CONTRADICTION
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discrete math notes CHAPTER 1 Axiomatic Method - using assumptions of true propositions to form a new conclusion. Axioms - propositions that are accepted as true. Corollary - a proposition that follows just a few logical steps...
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Theorems (2.1-2.5) - created from Mind Map Congruent Supplements and Complements #4: If angles are supplementary to the same angle then they are congruent #5 If angles are supplementary to congruent angles, then they are congruent #6 If angles are complementar...
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STRATEGY FOR MATHEMATICAL PROOF - created from Mind Map DIRECT PROOF CONTRAPOSITIVE CONTRADICTION
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Mathematical Induction Induction is a powerful way of proving known results. Method Let P˅n be the statement to be proved Assume that the result works for n=k i.e. P˅k is true Then show the result works for n=k+1 Show the result works for n...
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crying <3
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Mathematical Induction How to solve a mathematical problem? -Read carefully and make sure you understand what is being asked. To make sure you understand: -What is unknown? -What are the given quantities? -What are the given condition...
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1_STRATEGY FOR MATHEMATICAL PROOF - created from Mind Map DIRECT PROOF CONTRAPOSITIVE CONTRADICTION
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Mathematics for Computer Science Introduction and proofsA mathematical proof of a proposition is a chain of logical deductions leading to the proposition from a base set of axiomsPropositionImplicationAxiomComplete at April 09, 2016
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Proving methods - created from Mind Map Direct proof Mathematical Induction Indirect method
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Direct Proofs Click for Notes By Kashif Nazir
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Reasoning Topics - created from Mind Map Analogy classification coding-decoding
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Methods of Mathematics Proof - created from Mind Map Direct Method Used to prove conditional statement(If p(fact),then q(to be proved) ) Outline
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Unit 2: reasoning and proof Vocab:conjecture: conclusion resulted from using inductive reasoningcounterexample: the one example it takes to prove a conjecture wronginductive reasoning: the process of finding a pattern to solve a problem Vocab:co...
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About logic and mathematical proof notes
GoConqr OriginalLogic and mathematical proof notes
These notes cover ways to express and prove statements. The note on if-then statements and converses introduces hypotheses and conclusions. Other notes look at direct proof, contrapositives, contradiction and induction. There are also notes on geometry theorems and on axioms and logical deductions in computer science.
For a starting point, try Conclusions. It brings together properties and postulates used in reasoning, including equality and partition. If you are looking for a particular proof method, Mathematical Induction sets out an induction approach.
Revise with notes
Read a section, then close it and write down the steps of the argument in your own words. Reopen the note to check what you missed. If you want a visual overview, switch to a mind map on the unit page; when you are ready to test your reasoning, try a quiz there. Choose a note and work through a method at your own pace.
Frequently asked questions
Which note should I start with?
Conclusions is a useful starting point if you want to review properties and postulates used in reasoning. It includes equality and partition. For a focus on how statements are formed, the note on if-then statements and converses explains hypotheses and conclusions.
Do the notes cover different proof methods?
Yes. The listed notes include material on direct proof, contrapositives, contradiction and mathematical induction. Mathematical Induction sets out an induction method, while another note describes proof by exhaustion. You can choose a note according to the method you want to review.
Are these notes free to use?
Yes. Every note listed on this page is free to open and study without an account. The resources were made by GoConqr users. A free account also lets you make your own notes, quizzes, mind maps and flashcards, and save your quiz scores.