krainaksiazek the language of the mathematical proof the logical reasoning of mathematics 20039544
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Explanation and Proof in Mathematics Springer, Berlin
Książki / Literatura obcojęzyczna
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles).§A sampling of the coverage:§§The conjoint origins of proof and theoretical physics in ancient Greece.§Proof as bearers of mathematical knowledge.§Bridging knowing and proving in mathematical reasoning.§The role of mathematics in long-term cognitive development of reasoning.§Proof as experiment in the work of Wittgenstein.§Relationships between mathematical proof, problem-solving, and explanation.§Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Mathematical foundations>Mathematical logic
Features An Approach To The Teaching Of Mathematical Logic By Putting It In The Context Of The Puzzles And Paradoxes Of Common Language And Rational Thought. Using The Logic Of Lying And Truth-telling, This Book Introduces The Informal Reasoning Preparing Them For The Formal Study Of Symbolic Logic, From Propositional Logic To First-order Logic.
Mathematical Thinking PEARSON
Książki / Literatura obcojęzyczna
For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.
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1. Sklepy z krainaksiazek pl the language of the mathematical proof the logical reasoning of mathematics 20039544
t1=0.082, t2=0, t3=0, t4=0, t=0.083