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Mathematical Constants II [Kietas viršelis]

(Massachusetts Institute of Technology)
  • Formatas: Hardback, 782 pages, aukštis x plotis x storis: 241x160x46 mm, weight: 1270 g, Worked examples or Exercises; 32 Tables, black and white; 32 Halftones, black and white; 47 Line drawings, black and white
  • Serija: Encyclopedia of Mathematics and its Applications
  • Išleidimo metai: 06-Dec-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108470599
  • ISBN-13: 9781108470599
Kitos knygos pagal šią temą:
Mathematical Constants IIDidesnis paveikslėlis
  • Formatas: Hardback, 782 pages, aukštis x plotis x storis: 241x160x46 mm, weight: 1270 g, Worked examples or Exercises; 32 Tables, black and white; 32 Halftones, black and white; 47 Line drawings, black and white
  • Serija: Encyclopedia of Mathematics and its Applications
  • Išleidimo metai: 06-Dec-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1108470599
  • ISBN-13: 9781108470599
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781108470599.html
Raktažodžiai:
Famous mathematical constants include the ratio of circular circumference to diameter, p = 3.14 …, and the natural logarithm base, e = 2.718 …. Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

The author continues his outstanding scholarly attempt to bring together all significant mathematical constants in one place. Using this book, students and professionals will discover hidden links between apparently disconnected fields of inquiry. Unsolved problems - the lifeblood of mathematics - appear virtually everywhere as well.

Recenzijos

'Like the best sequels, this one covers similar ground to the original but finds ways to stay fresh and interesting any mathematician or math student who picks it up and spends a few minutes with it is likely to find something that is new and of interest to them. Finch has once again written a collection of essays about a wide range of topics that I expect I will enjoy flipping through for another decade and a half until I look forward to having Volume III land on my desk.' Darren Glass, MAA reviews 'This is a remarkable book [ which] can be thought of as a collection of essays that recount stories that are both successful and tangible.' Paul F. Bracken, MathSciNet 'Some of the most intriguing formulas of mathematics (like those of Ramanujan) adorn this treasure trove of mathematical gems Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants contain a total of 269 meticulously documented essays from all fields of mathematics.' Osmo Peokonen, The Mathematical Intelligencer 'Taken together, Mathematical Constants and Mathematical Constants II form a comprehensive and unique work that is a welcome addition to the mathematician's reference library.' Steven R. Finch, Notices of the AMS 'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical Gazette 'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical Gazette

Daugiau informacijos

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Preface ix
Notation xi
1 Number Theory and Combinatorics
1(271)
1.1 Bipartite, k-Colorable and k-Colored Graphs
1(6)
1.2 Transitive Relations, Topologies and Partial Orders
7(5)
1.3 Series-Parallel Networks
12(9)
1.4 Two Asymptotic Series
21(11)
1.5 Multiples and Divisors
32(8)
1.6 Discrepancy and Uniformity
40(9)
1.7 Unitarism and Infinitarism
49(7)
1.8 Erdos'Minimum Overlap Problem
56(2)
1.9 Planar Graph Growth Constants
58(9)
1.10 Tauberian Constants
67(5)
1.11 Integer Partitions
72(6)
1.12 Class Number Theory
78(19)
1.13 Quadratic Dirichlet L-Series
97(15)
1.14 Elliptic Curves over Q
112(20)
1.15 Modular Forms on SL2(Z)
132(15)
1.16 Chebyshev's Bias
147(2)
1.17 Pattern-Avoiding Permutations
149(5)
1.18 Cyclic Group Orders
154(3)
1.19 Dedekind Eta Products
157(3)
1.20 Series involving Arithmetric Functions
160(16)
1.21 Riemann Zeta Moments
176(6)
1.22 Central Binomial Coefficients
182(7)
1.23 Fractional Parts of Bernoulli Numbers
189(3)
1.24 Products of Consecutive-Integer Ratios
192(3)
1.25 Prime Number Theorem
195(7)
1.26 Mertens' Formula
202(4)
1.27 Cyclotomic Polynomials
206(1)
1.28 Minkowski--Alkauskas Constant
207(2)
1.29 Two-Colorings of Positive Integers
209(4)
1.30 Signum Equations and Extremal Coefficients
213(4)
1.31 Monoids of Natural Numbers
217(6)
1.32 Primitive Cusp Form
223(9)
1.33 Cubic and Quartic Characters
232(8)
1.34 Distribution of Error Terms
240(2)
1.35 Cilleruelo's LCM Constants
242(2)
1.36 Amicable Pairs and Aliquot Sequences
244(3)
1.37 Fermat Numbers and Elite Primes
247(2)
1.38 Average Least Nonresidues
249(4)
1.39 Apollonian Circles with Integer Curvatures
253(5)
1.40 Molteni's Composition Constant
258(2)
1.41 Boolean Decision Functions
260(3)
1.42 Map Asymptotics Constant
263(3)
1.43 Injections, Surjections and More
266(6)
2 Inequalities and Approximation
272(105)
2.1 Hardy--Littlewood Maximal Inequalities
272(3)
2.2 Bessel Function Zeroes
275(9)
2.3 Nash's Inequality
284(7)
2.4 Uncertainty Inequalities
291(4)
2.5 Airy Function Zeroes
295(4)
2.6 Projections of Minimal Norm
299(4)
2.7 Bohr's Inequality
303(3)
2.8 Moduli of Continuity
306(5)
2.9 Quinn-Rand-Strogatz Constant
311(3)
2.10 Tsirelson's Constant
314(7)
2.11 Mathieu Eigenvalues
321(3)
2.12 Thomas--Fermi Model
324(5)
2.13 Prandtl--Blasius Flow
329(9)
2.14 Lane--Ritter--Emden Constants
338(6)
2.15 Radiative Transfer Equations
344(8)
2.16 Carleman's Inequality
352(2)
2.17 Golay--Littlewood Problem
354(4)
2.18 Online Matching Coins
358(5)
2.19 Toothpicks and Live Cells
363(2)
2.20 Virial Coefficients
365(8)
2.21 Strong Triangle Inequality
373(4)
3 Real and Complex Analysis
377(78)
3.1 Radii in Geometric Function Theory
377(10)
3.2 Numerical Radii of Linear Operators
387(3)
3.3 Coefficient Estimates for Univalent Functions
390(9)
3.4 Planar Harmonic Mappings
399(4)
3.5 Constant of Interpolation
403(3)
3.6 Dirichlet Integral
406(1)
3.7 Brachistochrone Problem
407(3)
3.8 Unconditional Basis Constants
410(4)
3.9 Power Series with Restricted Coefficients
414(1)
3.10 Hankel and Toeplitz Determinants
415(4)
3.11 Goldberg's Zero-One Constants
419(4)
3.12 Electrical Capacitance
423(5)
3.13 Aissen's Convex Set Function
428(2)
3.14 Condition Numbers of Matrices
430(2)
3.15 Goddard's Rocket Problem
432(5)
3.16 Swing-Up Control of a Pendulum
437(7)
3.17 Zermelo's Navigation Problem
444(11)
4 Probability and Stochastic Processes
455(168)
4.1 Hammersley's Path Process
455(7)
4.2 Moments of Sums
462(6)
4.3 Ornstein-Uhlenbeck Process
468(11)
4.4 Zero Crossings
479(6)
4.5 Variants of Brownian Motion
485(9)
4.6 Shapes of Binary Trees
494(10)
4.7 Expected Lifetimes and Inradii
504(7)
4.8 Subcritical Galton--Watson Trees
511(8)
4.9 Continued Fraction Transformation
519(8)
4.10 ContinuedFractionTransformation.il
527(6)
4.11 ContinuedFractionTransformation.nl
533(8)
4.12 ContinuedFractionTransformation.IV
541(11)
4.13 Lyapunov Exponents
552(6)
4.14 Lyapunov Exponents. II
558(6)
4.15 Lyapunov Exponents. Ill
564(4)
4.16 Lyapunov Exponents. IV
568(9)
4.17 Stars and Watermelons
577(3)
4.18 Prophet Inequalities
580(2)
4.19 Excursion Durations
582(2)
4.20 Gambler's Ruin
584(5)
4.21 Self-Convolutions
589(3)
4.22 Newcomb--Benford Law
592(2)
4.23 Electing a Leader
594(5)
4.24 Substitution Dynamics
599(5)
4.25 Biham--Middleton--Levine Traffic
604(1)
4.26 Contact Processes
605(7)
4.27 Interpolating between Max and Sum
612(4)
4.28 Mixing Time of Markov Chains
616(3)
4.29 Correlated Products
619(4)
5 Geometry and Topology
623(142)
5.1 Knots, Links and Tangles
623(9)
5.2 Convex Lattice Polygons
632(4)
5.3 Volumes of Hyperbolic 3-Manifolds
636(7)
5.4 Poisson--Voronoi Tessellations
643(9)
5.5 Optimal Escape Paths
652(2)
5.6 Minkowski--Siegel Mass Constants
654(6)
5.7 Slicing Problem
660(2)
5.8 Constant of Theodorus
662(2)
5.9 Nearest--Neighbor Graphs
664(4)
5.10 Random Triangles
668(14)
5.11 Random Triangles. II
682(7)
5.12 Random Triangles. III
689(6)
5.13 Random Triangles. IV
695(5)
5.14 Random Triangles. V
700(13)
5.15 Random Triangles. VI
713(5)
5.16 Colliding Dice Probabilities
718(3)
5.17 Gergonne--Schwarz Surface
721(10)
5.18 Partitioning Problem
731(9)
5.19 Soap Film Experiments
740(7)
5.20 Inflating an Inelastic Membrane
747(3)
5.21 Enumerative Geometry
750(4)
5.22 Distance-Avoiding Sets in the Plane
754(3)
5.23 Fraenkel Asymmetry
757(8)
Index 765
Steven R. Finch is Research Computing Specialist at the Massachusetts Institute of Technology, Sloan School of Management. He is honoured to have received a Book Fellowship from the Clay Mathematics Institute and a Ford award for expository excellence. After the publication of the first volume of Mathematical Constants (Cambridge, 2003), he worked for three years as a statistical programmer at the Boston University School of Public Health, and then taught for ten years as a preceptor at the Harvard University Department of Statistics.