000			02662nam a22002897a 4500
003			OSt
005			20250317173443.0
008			250317b |||||||| |||| 00| 0 hin d
020			_a9781498775250
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	0	_a510.6 _bDEA-B
100	1		_aDeaconu, Valentin
245	1	2	_aBridge to higher mathematics
260			_aBoca Raton : _bCRC Press, Taylor & Francis Group, _c2017.
300			_axiv, 203 pages : _billustrations ; _c24 cm.
490	0		_aTextbooks in mathematics
500			_a"A Chapman & Hall book."
504			_aIncludes bibliographical references and index.
520			_aA Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.
650		0	_aProof theory _vTextbooks
650		0	_aLogic, symbolic and mathematical _vTextbooks
650		0	_aMathematics _vTextbooks
700	1		_aPfaff, Donald C.
856			_3Table of content _uhttps://www.routledge.com/A-Bridge-to-Higher-Mathematics/Deaconu-Pfaff/p/book/9781498775250?srsltid=AfmBOorcyXMF46D204vSbRsY7oaVq-WJj576MHLKetL6gE-Z37SspMqi#googlePreviewContainer
856			_3Reviews _uhttps://www.goodreads.com/book/show/28755712-a-bridge-to-higher-mathematics?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cBK
999			_c35929 _d35929