A Transition to Advanced Mathematics
Successfully addressing the frustration many students feel as they make the transition from beginning calculus to a more rigorous level of mathematics, A Transition to Advanced Mathematics provides a firm foundation in the major ideas needed for continued work in the discipline. The authors guide students to think and to express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. With their proven approach, Smith, Eggen, and St. Andre introduce students to rigorous thinking about sets, relations, optional functions and cardinality, and present introductions to modern algebra and analysis with sufficient depth to capture some of their spirit and characteristics. Addressing the needs of different students, A Transition to Advanced Mathematics includes exercises of varying difficulty for each section and provides worked-out answers to selected problems. With its straightforward style, logical topic sequence, exceptionally clear writing, well-chosen examples, illustrations, and historical notes, this unparalleled text will improve mathematical fashion, thereby giving your students a solid understanding of the material most useful for advanced courses.
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A D B A U B A X B abelian accumulation point Assign a grade Assume Axiom of Choice Bolzano-Weierstrass Theorem cardinal number Claim codomain contradiction contrapositive countable countable sets cyclic group defined DEFINITION Let digraph direct proof divides domain equivalence class equivalence relation exercise exists F F F F failure F T F false Figure finite set function Give an example graph Heine-Borel Theorem Hint homomorphism identity implies induction infinite set integers inverse irrational isomorphic Let G mathematics natural number normal subgroup number of elements ordered pairs P A Q pairwise disjoint partial order partition permutation positive integer prime Proofs to Grade propositional forms quotient group rational numbers reflexive sequence statement subgroup of G Suppose symbols symmetric tautology tify assignments true truth table vertex vertices