A Transition to Advanced Mathematics
Cengage Learning, Jun 1, 2010 - Mathematics - 416 pages
A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.
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abelian accumulation point algebraic system assignments of grades Assume Axiom of Choice bijection Bolzano–Weierstrass Theorem cardinal number choose Claim codomain compute contradiction contrapositive countable sets defined DEFINITIONS Let denumerable digits digraph direct proof divides divisor domain equivalence classes equivalence relation Exercise exists F failure F T F false Figure finite set Give an example graph Heine–Borel Theorem Hint homomorphism implies induction infinite set inverse irrational Lemma mathematics multiplication natural number nonempty set number greater number of elements one-to-one correspondence ordered field ordered pairs pairwise disjoint partial order partially correct partition permutation positive integer positive real number Proofs to Grade proposition Prove quantified rational numbers real numbers reflexive Rng f Section sentence sequence Suppose symmetric Theorem transitive truth table truth value universe vertex vertices write