Discrete Mathematics—Introduction
... Show that the difference between a rational number and an irrational number is an irrational number. [Can you do this with a direct proof?] Proof: (by contradiction) Suppose there is a rational number r and an irrational number s such that r-s is rational. So r = a/b where a and b are integers and b ...
... Show that the difference between a rational number and an irrational number is an irrational number. [Can you do this with a direct proof?] Proof: (by contradiction) Suppose there is a rational number r and an irrational number s such that r-s is rational. So r = a/b where a and b are integers and b ...
1.1 Patterns and Inductive Reasoning
... Inductive reasoning is very important to the study of mathematics. You look for a pattern in specific cases and then you write a conjecture that you think describes the general case. Remember, though, that just because something is true for several specific cases does not prove that it is true in ge ...
... Inductive reasoning is very important to the study of mathematics. You look for a pattern in specific cases and then you write a conjecture that you think describes the general case. Remember, though, that just because something is true for several specific cases does not prove that it is true in ge ...
Algebra I - Denise Kapler
... Known- from inside and outside the problem Unknown – what are you being asked to find Relationship – between known and unknown Solve Answer: Does it make sense? Plug it back in ...
... Known- from inside and outside the problem Unknown – what are you being asked to find Relationship – between known and unknown Solve Answer: Does it make sense? Plug it back in ...
Full text
... colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1 Fs+1 Ft+1 + Fr Fs Ft − Fr−1 Fs−1 Ft−1 . ...
... colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1 Fs+1 Ft+1 + Fr Fs Ft − Fr−1 Fs−1 Ft−1 . ...
OPEN DIOPHANTINE PROBLEMS 1. Diophantine Equations 1.1
... – that a complete answer to question (a) is not yet available. There is no algorithm (not even a conjectural one) to decide whether a curve has a rational point or not, – that a number of results are known about question (b), the latest work on this topic being due to G. Rémond [Re] who produces an ...
... – that a complete answer to question (a) is not yet available. There is no algorithm (not even a conjectural one) to decide whether a curve has a rational point or not, – that a number of results are known about question (b), the latest work on this topic being due to G. Rémond [Re] who produces an ...
List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.Some reasons why a particular publication might be regarded as important:Topic creator – A publication that created a new topicBreakthrough – A publication that changed scientific knowledge significantlyInfluence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith.