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Publication type: Book
Title:

Journey through genius : the great theorems of mathematics

Author(s): Dunham,William (Author)
Responsibility Data: William Dunham
Publication Data: New York : John Wiley and Sons, Inc., 1990
Physical Description: xiii, 300 p, : ill. ; 24 cm.
Series Data: Wiley science editions;
ISBN: 0-471-50030-5  
Subject Area: Mathematics
Subject Terms:  Mathematics -- History   Mathematicians -- Biography 
Call Number: 510.9 DUN
Accession Number 30472

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Publication type: Book
Title:

Men of mathematics

Author(s): Bell,E. T. (Author)
Responsibility Data: by E. T. Bell
Publication Data: New York : Simon & Schuster, 1986
Physical Description: xvii, 590 p. ; 21 cm.
ISBN: 0-671-62818-6  
Subject Area: Mathematics
Subject Terms:  Mathematicians   Mathematics -- History 
Call Number: 510.92 BEL
Accession Number 73489

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Publication type: Book
Title:

An episodic history of mathematics: mathematical culture through problem solving

Author(s): Krantz,Steven G. (Author)
Responsibility Data: Steven G. Krantz
Publication Data: USA : The Mathematical Association of America , 2010
Physical Description: xiii, 381 p. : ill. ; 24 cm.
Notes: Includes bibliographical references and indexes.
ISBN: 978-0-88385-766-3  
Subject Area: Mathematics
Subject Terms:  Mathematics -- History -- Study and teaching (Higher)   Mathematics -- Problems, exercises, etc.   Mathematics -- Study and teaching (Higher)   Mathematicians 
Call Number: 510.9 KRA
Accession Number 165770

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Date:09/05/24

 

Publication type: Academic journal
Title:

The American mathematical monthly

Publication Data: Washington , US : MAA, 2019-
Frequency:
ISSN: 0002-9890
Subject Area: Mathematics
Subject Terms:  Mathematics -- Periodicals   Mathematics -- Bibliography -- Periodicals   Mathematicians -- Periodicals 
Call Number: 510.5 AMM
Accession Number 174107
Issue(s) Information: Received:10 \ Article(s) indexed:23

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  2019 v.126 , n.4-6 145962 145962 Available References & Periodical Hall - 2nd floor
  2019 v.126 , n.1-3 145963 145963 Available References & Periodical Hall - 2nd floor
  2019 v.126 , n.7-8 145964 145964 Available References & Periodical Hall - 2nd floor
  2019 v.126 , n.9-10 145965 145965 Available References & Periodical Hall - 2nd floor
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Publication type: Article
Title:

Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2019 to Philip Uri Treisman for Distinguished Service to Mathematics

Author(s): Peeples,Joanne (Author) Alvarez,James (Author) Charney,Ruth (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 MAR V.126 N.3
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 195-198
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177077
Abstract
--- ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1551605
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Publication type: Article
Title:

Differences of Bijections

Author(s): H. Ullman,Daniel (Author) J. Velleman,Daniel (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 MAR V.126 N.3
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 199-216
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177078
Abstract
When is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling. A theorem of Marshall Hall settles the question for finite abelian groups ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1546077
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Publication type: Article
Title:

Two Binomial Identities of Ruehr Revisited

Author(s): Allouche,J.-P (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 MAR V.126 N.3
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 217-225
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177079
Abstract
A curious identity, proposed by Kimura and proved by Kimura, Ruehr and others, involves two definite integrals of the same continuous function f composed with the polynomial 3x2?2x3. In his proof Ruehr indicates ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1546079
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Publication type: Article
Title:

Equidistribution of Zeros of Polynomials

Author(s): Soundararajan,K (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 MAR V.126 N.3
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 226-236
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177080
Abstract
A classical result of Erd?s and Tur?n states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier analysis we give a short and self-contained proof of this result. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1546078
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Publication type: Article
Title:

The Round Taylor Method

Author(s): M. Perdomo,Oscar (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 MAR V.126 N.3
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 237-251
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177081
Abstract
This article provides a numerical method for providing approximate solutions to initial-value differential equations. Even though this method is a small modification of the Taylor series method, it provides several advantages. Besides the traditional parameter h=?t used in most numerical methods, ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1546087
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Publication type: Article
Title:

Proof of the Sheldon Conjecture

Author(s): Pomerance,Carl (Author) Spicer,Chris (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/OCT V.126 N.8
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 688-698
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177082
Abstract
In [3], the authors introduce the concept of a Sheldon prime, based on a conversation between several characters in the CBS television situation comedy The Big Bang Theory. The authors of [3] leave open the question of whether 73 is the unique Sheldon prime. This article answers this question in the affirmative. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1626672
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Publication type: Article
Title:

Consensus and Fragmentation of Opinions with a Focus on Bounded Confidence

Author(s): Hegselmann,Rainer (Author) Krause,Ulrich (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/OCT V.126 N.8
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 700-716
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177083
Abstract
During the last several years opinion dynamics, in particular the question of a consensus, have been studied by many researchers across various disciplines, ranging from physics, computer science, and electrical engineering to biology, economics ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1626685
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Publication type: Article
Title:

Fourier Transform Inversion Using an Elementary Differential Equation and a Contour Integral

Author(s): Talvila,Erik (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/OCT V.126 N.8
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 717-727
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177084
Abstract
Let f be a function on the real line. The Fourier transform inversion theorem is proved under the assumption that f is absolutely continuous such that f and f' are Lebesgue integrable. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1632629
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Publication type: Article
Title:

Perfect Squares as Concatenation of Consecutive Integers

Author(s): Luca,Florian (Author) Stanica,Pantelimon (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/OCT V.126 N.8
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 728-734
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 177085
Abstract
We find an infinite family of positive integers a such that concatenating a and a – 1 in base 10 (from left to right) results in a number that is a perfect square and estimates for such concatenations. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1632628
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Publication type: Article
Title:

Random Triangles and Polygons in the Plane

Author(s): Cantarella,Jason (Author) Needham,Tom (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 FEB V.126 N.2
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 113-134
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 179820
Abstract
In 1997, Jean-Claude Hausmann and Allen Knutson introduced a natural and beautiful correspondence between planar n-gons and the Grassmann manifold of 2-planes in real n-space. This construction leads to a natural probability distribution and a natural metric on polygons which has been used in shape classification and computer vision. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1535735
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Publication type: Article
Title:

Newton Quadrilaterals, the Associated Cubic Equations, and Their Rational Solutions

Author(s): Hajja,Mowaffaq (Author) Sondow,Jonathan (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 FEB V.126 N.2
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 135-150
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 179821
Abstract
A Newton quadrilateral is a convex quadrilateral inscribed in a circle, with one side a diameter. For diameter d and the other side lengths a,b,andc, Newton arrived at the cubic equation d3-(a2+b2+c2)d-2abc=0, which we shall refer to as Newton’s equation. Its positive integer solutions were found by P. Bachmann. All (positive and nonpositive) integer solutions were found by A. Oppenheim in terms of logarithmic and hyperbolic functions. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1537426
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Publication type: Article
Title:

Characterizations of the Euclidean Ball by Intersections with Planes and Slabs

Author(s): Jerónimo-Castro,J. (Author) Yee-Romero,C. (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019 FEB V.126 N.2
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 151-157
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 179822
Abstract
In this article we prove two characterizations of the Euclidean ball: (i) the only convex body in R3 such that every normal plane bisects the volume (or surface area) is the Euclidean ball, (ii) the only convex body K in R3 such that for two suitable values h1, h2, the surface area of the intersection between any slab of width hi, and ?K is a constant ci, i=1,2, is the Euclidean ball. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1537759
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Publication type: Article
Title:

The Calkin–Wilf Tree of a Quadratic Surd

Author(s): Ponton,Lionel
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 771-785
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180819
Abstract
By using the Calkin–Wilf tree, we prove the irrationality of numbers of the form a=(N--v+p)/q where N is a positive integer that is not a perfect square, p is a rational integer such that p2
Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1644123
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Publication type: Article
Title:

Fibonacci Numbers, Integer Compositions, and Nets of Antiprisms

Author(s): Mabry,Rick (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 786-801
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180820
Abstract
All geometrically distinct nets (edge-unfoldings) are explicitly constructed for the infinite family of polyhedra known as uniform antiprisms. The Fibonacci numbers F2n are shown to count the number of nets of the n-antiprism that have point symmetry. (The n-antiprism refers to the antiprism whose surface consists of two regular n-gons separated by a band of 2n equilateral triangles.) Smaller evenly indexed Fibonacci numbers count certain subfamilies of these nets. Well-known formulas for sums of alternately indexed Fibonacci numbers motivate and become accessories to our constructions and proofs. For counting and constructing the symmetric nets, we first use a known result connecting compositions of integers and Fibonacci numbers. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1644124
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Publication type: Article
Title:

On Erdos’s Last Equation

Author(s): Shiu,Peter (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 802-808
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180821
Abstract
We call x1x2?xn=n(x1+x2+?+xn) Erdos’s last equation, and establish sharp upper bounds for xn-1 and xn. Partitioning the solutions into classes Cl(n), where l+1 is the number of xi>1, a heuristic argument is given to support the conjecture that Cl(n) is nonempty for all large enough n, depending on l. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1639466
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Publication type: Article
Title:

Operator-valued Extensions of Matrix-norm Inequalities

Author(s): Jameson,G. J. O. (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 809-815
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180822
Abstract
We describe a rather striking extension of a wide class of inequalities. Some famous classical inequalities, such as those of Hardy and Hilbert, equate to the evaluation of the norm of a matrix operator. Such inequalities can be presented in two versions, linear and bilinear. We show that in all such inequalities, the scalars can be replaced by operators on a Hilbert space, with the conclusions taking the form of an operator inequality in the usual sense. With careful formulation, a similar extension applies to the Cauchy–Schwarz inequality. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1639467
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Publication type: Article
Title:

Dimension of Random Limsup Sets

Author(s): Ekström,Fredrik (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 816-824
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180823
Abstract
The Hausdorff dimension of the set of points that are covered infinitely many times by a sequence of randomly distributed balls can be expressed in terms of the sizes of the balls. In this article, a new proof of the formula is presented. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1640528
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Publication type: Article
Title:

Partitioning the Real Line into an Uncountable Collection of Everywhere Uncountably Dense Sets

Author(s): Zimmerman,Seth (Author) Ho,Chungwu (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/NOV V.126 N.9
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 825-834
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 180824
Abstract
A recent paper showed that given any positive integer k, the real line can be partitioned into k subsets, each of which is uncountable in every nonempty open interval in the real line. This article extends that result to show that the real line can be partitioned into an uncountable collection of such subsets, all but one of which have measure zero. This seems to be of interest in its own right since most of the well-known sets of measure zero are either countable or not dense. It is then shown that each of the sets in the partition can be partitioned further into an uncountable collection of subsets that are again uncountable in every nonempty open set of the real line. Indeed, this process can be repeated infinitely many times. Finally, all of the results for the real line are shown to extend to n-dimensional Euclidean spaces and to the classical lp spaces. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1640529
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Publication type: Article
Title:

Absent-Minded Passengers

Author(s): Henze,Norbert (Author) Last,Gunter (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/DEC V.126 N.10
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 867-875
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 181078
Abstract
Passengers board a fully booked airplane in order. The first passenger picks one of the seats at random. Each subsequent passenger takes his or her assigned seat if available, otherwise takes one of the remaining seats at random. It is well known that the last passenger obtains her own seat with probability 1/2. We study the distribution of the number of incorrectly seated passengers, and we also discuss the case of several absent-minded passengers. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1656024
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Publication type: Article
Title:

A Hot Spot Proof of the Generalized Wall Theorem

Author(s): Bergelson,Vitaly (Author) Vandehey,Joseph (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/DEC V.126 N.10
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 876-890
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 181079
Abstract
If a sequence of numbers behaves like a random sequence, do we expect subsequences to also behave like a random sequence? Wall proved that normality of a base-b expansion is preserved along arithmetic progressions. What makes arithmetic progressions special is that they are deterministic sequences, a type of low-complexity sequence. We give a self-contained proof that selection along deterministic sequences preserves normality and provide several interesting examples of nontrivial deterministic sequences. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1651166
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Publication type: Article
Title:

A Positivity Conjecture Related to the Riemann Zeta Function

Author(s): Bellemare,Hugues (Author) Langlois,Yves (Author) Ransford,Thomas (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/DEC V.126 N.10
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 891-904
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 181080
Abstract
According to two remarkable theorems of Nyman and Báez-Duarte, the Riemann hypothesis is equivalent to a simply stated criterion concerning least-squares approximation. In carrying out computations related to this criterion, we have observed a curious phenomenon: for no apparent reason, at least the first billion entries of a certain infinite triangular matrix associated with the Riemann zeta function are all positive. In this article, we describe the background leading to this observation, and make a conjecture ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1651165
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Publication type: Article
Title:

Too Acute to Be True: The Story of Acute Sets

Author(s): Gerencsér,Balezs (Author) Harangi,Viktor (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/DEC V.126 N.10
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 905-914
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 181081
Abstract
Erdos asked to give as many points in Rd as possible such that all angles formed by the points are acute. For decades the progress had been slow before a number of twists took place recently. We tell the story, sketching all the various constructions. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1655311
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Publication type: Article
Title:

Halving the Bounds for the Markov, Chebyshev, and Chernoff Inequalities Using Smoothing

Author(s): Huber,Mark (Author)
Source Journal Info. Title:The American mathematical monthly
Issue Number:2019/DEC V.126 N.10
Call No.:510.5 AMM
Location: References & Periodical Hall - 2nd floor
Physical Description: p 915-927
Subject Area: Mathematics
Subject Terms:  Mathematics   Mathematics -- Bibliography   Mathematicians 
Accession Number 181082
Abstract
The Markov, Chebyshev, and Chernoff inequalities are some of the most widely used methods for bounding the tail probabilities of random variables. In all three cases, the bounds are tight in the sense that there exists easy examples where the inequalities become equalities. Here we will show, through a simple smoothing using auxiliary randomness, that each of the three bounds can be cut in half. In many common cases, the halving can be achieved without the need for the auxiliary randomness. ...

Abstract URL:https://www.tandfonline.com/doi/full/10.1080/00029890.2019.1656484

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