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082 0 4 _a512.7
_223
049 _aMAIN
100 1 _aAsh, Avner,
_d1949-
_964747
245 1 0 _aSumming it up :
_bfrom one plus one to modern number theory /
_cAvner Ash and Robert Gross.
264 1 _aPrinceton :
_bPrinceton University Press,
_c[2016]
264 4 _c�20
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
347 _bPDF
504 _aIncludes bibliographical references and index.
588 0 _aPrint version record.
520 _aWe use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series--long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+ ... =? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
505 0 0 _tFrontmatter --
_tCONTENTS --
_tPREFACE --
_tACKNOWLEDGMENTS --
_tINTRODUCTION: WHAT THIS BOOK IS ABOUT --
_tPART ONE. FINITE SUMS --
_tCHAPTER 1. PROEM --
_tCHAPTER 2. SUMS OF TWO SQUARES --
_tCHAPTER 3. SUMS OF THREE AND FOUR SQUARES --
_tCHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM --
_tCHAPTER 5. SIMPLE SUMS --
_tCHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA --
_tPART TWO. INFINITE SUMS --
_tCHAPTER 7. INFINITE SERIES --
_tCHAPTER 8. CAST OF CHARACTERS --
_tCHAPTER 9. ZETA AND BERNOULLI --
_tCHAPTER 10. COUNT THE WAYS --
_tPART III. MODULAR FORMS AND THEIR APPLICATIONS --
_tCHAPTER 11. THE UPPER HALF-PLANE --
_tCHAPTER 12. MODULAR FORMS --
_tCHAPTER 13. HOW MANY MODULAR FORMS ARE THERE? --
_tCHAPTER 14. CONGRUENCE GROUPS --
_tCHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED --
_tCHAPTER 16. MORE THEORY OF MODULAR FORMS --
_tCHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS --
_tBIBLIOGRAPHY --
_tINDEX.
546 _aIn English.
590 _aIEEE
_bIEEE Xplore Princeton University Press eBooks Library
600 0 7 _aMathematik.
_2gnd
_964748
650 0 _aNumber theory.
_913208
650 0 _aMathematics
_vPopular works.
_964749
650 6 _aTh�eorie des nombres.
_964750
650 6 _aMath�ematiques
_vOuvrages de vulgarisation.
_964751
650 7 _aMATHEMATICS
_xAlgebra
_xIntermediate.
_2bisacsh
_964159
650 7 _aMATHEMATICS
_xGeneral.
_2bisacsh
_94635
650 7 _aMathematics.
_2fast
_0(OCoLC)fst01012163
_911584
650 7 _aNumber theory.
_2fast
_0(OCoLC)fst01041214
_913208
650 7 _aAddition
_2gnd
_964752
650 7 _aZahl
_2gnd
_964753
650 7 _aZahlentheorie
_2gnd
_964754
650 7 _aPhilosophie
_2gnd
_964755
655 4 _aElectronic books.
_93294
655 7 _aPopular works.
_2fast
_0(OCoLC)fst01423846
_96581
655 7 _aObras de divulgaci�on.
_2lcgft
_964756
700 1 _aGross, Robert,
_d1959-
_964757
776 0 8 _iPrint version:
_aAsh, Avner, 1949-
_tSumming it up.
_dPrinceton : Princeton University Press, [2016]
_z9780691170190
_w(DLC) 2015037578
_w(OCoLC)922970903
856 4 0 _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452511
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