An Invitation to Combinatorics

2021 ◽  
Author(s):  
Shahriar Shahriari
Keyword(s):  
Stirling Numbers ◽  
Exclusion Principle ◽  
Open Problems ◽  
Warm Up ◽  
Calculus Sequence ◽  
Award Winning ◽  
Self Study ◽  
Conversational Style ◽  
The Subject ◽  
Partitions Of Integers

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

scholarly journals Indigenous Water Rights in Comparative Law

2020 ◽  
Vol 9 (3) ◽  
pp. 393-402
Author(s):  
Elizabeth Macpherson
Keyword(s):  
Human Population ◽  
Global Financial Crisis ◽  
Water Rights ◽  
The United States ◽  
Wall Street ◽  
Award Winning ◽  
The Subject ◽  
Academy Award ◽  
Increasing Demand ◽  
Poor Management

At the end of the 2015 Academy Award-winning film The Big Short, which explores the origins of the 2008 Global Financial Crisis, a caption notes that the Wall Street investor protagonist of the film who predicted the collapse of the United States (US) housing market would now be ‘focused on one commodity: water’. Water is sometimes described in popular culture as ‘the new oil’ or ‘more valuable than gold’. It is predicted to be the subject of increasing uncertainty, competition, conflict, and even war, as increasing demand from a growing human population and development meets reduced supply as a result of poor management, overuse, and climate change.

History and Theory in Anthropology

2021 ◽  
Author(s):  
Alan Barnard
Keyword(s):  
North America ◽  
New Developments ◽  
The Past ◽  
Award Winning ◽  
The World ◽  
The Subject ◽  
Post Colonialism ◽  
New Generation ◽  
History And Theory

In the past twenty years, there have been exciting new developments in the field of anthropology. This second edition of Barnard's classic textbook on the history and theory of anthropology has been revised and expanded to include up-to-date coverage on all the most important topics in the field. Its coverage ranges from traditional topics like the beginnings of the subject, evolutionism, functionalism, structuralism, and Marxism, to ideas about globalization, post-colonialism, and notions of 'race' and of being 'indigenous'. There are several new chapters, along with an extensive glossary, index, dates of birth and death, and award-winning diagrams. Although anthropology is often dominated by trends in Europe and North America, this edition makes plain the contributions of trendsetters in the rest of the world too. With its comprehensive yet clear coverage of concepts, this is essential reading for a new generation of anthropology students.

Milnor's conjecture on monotonicity of topological entropy: Results and questions

2014 ◽  
Author(s):  
Sebastian van Strien
Keyword(s):  
Topological Entropy ◽  
State Of The Art ◽  
Rigidity Theorem ◽  
Real Polynomial ◽  
Open Problems ◽  
Polynomial Maps ◽  
History Of ◽  
The Subject ◽  
Quadratic Case ◽  
Real Polynomial Maps

This chapter discusses Milnor's conjecture on monotonicity of entropy and gives a short exposition of the ideas used in its proof. It discusses the history of this conjecture, gives an outline of the proof in the general case, and describes the state of the art in the subject. The proof makes use of an important result by Kozlovski, Shen, and van Strien on the density of hyperbolicity in the space of real polynomial maps, which is a far-reaching generalization of the Thurston Rigidity Theorem. (In the quadratic case, density of hyperbolicity had been proved in studies done by M. Lyubich and J. Graczyk and G. Swiatek.) The chapter concludes with a list of open problems.

Local Algorithms for Topology Control in Ad-Hoc Networks

2010 ◽  
pp. 51-58
Author(s):  
Evangelos Kranakis ◽  
Jorge Urrutia
Keyword(s):  
Topology Control ◽  
Ad Hoc ◽  
Edge Coloring ◽  
Dominating Sets ◽  
Open Problems ◽  
Local Algorithms ◽  
Trade Offs ◽  
The Subject ◽  
Hoc Networks ◽  
Local Topology

In this chapter, we present a survey of recent techniques for local topology control in location aware Unit Disk Graphs including local algorithms for Routing, Traversal, Planar Spanners, Dominating and Connected Dominating Sets, and Vertex and Edge Coloring. In addition to investigating trade-offs for these problems, we discuss open problems that will play an important role in the future development of the subject.

scholarly journals Efficient Self-Heating in Nanowire Sensors: Prospects for Very-Low Power

Proceedings ◽  
2018 ◽  
Vol 2 (13) ◽  
pp. 829
Author(s):  
Cristian Fàbrega ◽  
Olga Casals ◽  
Joan Daniel Prades
Keyword(s):  
Gas Sensors ◽  
State Of The Art ◽  
Electronic Devices ◽  
Power Demand ◽  
Heating Effect ◽  
Warm Up ◽  
Self Heating ◽  
Probing Signal ◽  
The Subject ◽  
And Control

Self-heating operation, or the use of the resistance-probing signal to warm up and control the temperature of nanowire devices, has been the subject of research for more than a decade. The state-of-the-art shows that this approach is serving to lower the power demand in temperature-activated devices, especially in conductometric gas sensors, but the simplicity of eliminating the heating element comes with the complexity of integrating 1-dimensional nanomaterials in electronic devices. The advantages of the efficient self-heating effect in nanowires have already been probed in a broad range of systems and materials. But when it comes to transfer this operating principle to new systems and materials natural doubts arise: how to do it?, how much savings in power will be achieved? We will address these questions in this review contribution.

scholarly journals Holomorphic Legendrian curves

2017 ◽  
Vol 153 (9) ◽  
pp. 1945-1986 ◽  
Author(s):  
Antonio Alarcón ◽  
Franc Forstnerič ◽  
Francisco J. López
Keyword(s):  
Riemann Surface ◽  
Contact Structure ◽  
Existence Theorems ◽  
Contact Manifold ◽  
Open Problems ◽  
General Existence ◽  
The Subject ◽  
Complex Contact Manifold ◽  
Holomorphic Contact ◽  
Legendrian Curves

In this paper we study holomorphic Legendrian curves in the standard holomorphic contact structure on$\mathbb{C}^{2n+1}$for any$n\in \mathbb{N}$. We provide several approximation and desingularization results which enable us to prove general existence theorems, settling some of the open problems in the subject. In particular, we show that every open Riemann surface$M$admits a proper holomorphic Legendrian embedding$M{\hookrightarrow}\mathbb{C}^{2n+1}$, and we prove that for every compact bordered Riemann surface$M={M\unicode[STIX]{x0030A}}\,\cup \,bM$there exists a topological embedding$M{\hookrightarrow}\mathbb{C}^{2n+1}$whose restriction to the interior is a complete holomorphic Legendrian embedding${M\unicode[STIX]{x0030A}}{\hookrightarrow}\mathbb{C}^{2n+1}$. As a consequence, we infer that every complex contact manifold$W$carries relatively compact holomorphic Legendrian curves, normalized by any given bordered Riemann surface, which are complete with respect to any Riemannian metric on$W$.

scholarly journals The second dual of a Banach algebra

1979 ◽  
Vol 84 (3-4) ◽  
pp. 309-325 ◽  
Author(s):  
J. Duncan ◽  
S. A. R. Hosseiniun
Keyword(s):  
Banach Algebra ◽  
Open Problems ◽  
Current State ◽  
Second Dual ◽  
The Subject

SynopsisWe give a survey of the current state of knowledge on the Arens second dual of a Banach algebra, including some simplified proofs of known results, some new results, some open problems and a full bibliography of the subject.

Dyskusja nad rolą i zadaniami podręcznika szkolnego w Polsce w latach 1918–1939

2019 ◽  
Vol 63 (4(250)) ◽  
pp. 234-244
Author(s):  
Ewa Wołoszyn
Keyword(s):  
19Th Century ◽  
Educational Process ◽  
Dominant Position ◽  
Role Function ◽  
Self Study ◽  
The Subject

The subject of this article is a debate which took place in the community of teachers and educators over the period 1918–1939. Its topic related to the function and role of textbooks in the educational process. The analysis of the published articles and science books showed the evolution of views and opinions which developed from the extreme rejection of a textbook and the denial of its dominant position in a 19th century school, to a compromise that was reached in the 1930s and reconciled the “vivid teaching” of a teacher with students’ self-study with a textbook. Maturing and changing opinions and views on the issue of a textbook referred to its classification, role, function, contents structure and the language. The debate which took place in the Second Polish Republic did not result in developing the theory of a textbook although it was an important contribution to its shaping.

scholarly journals Tiling the Line with Triples

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Aaron Meyerowitz
Keyword(s):  
Greedy Algorithm ◽  
Direct Proof ◽  
Open Problems ◽  
One Dimensional ◽  
Proof By Contradiction ◽  
International Audience ◽  
The Subject ◽  
The One ◽  
Finite Digraph ◽  
Elegant Proof

International audience It is known the one dimensional prototile $0,a,a+b$ and its reflection $0,b,a+b$ always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph $D_{ab}$. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given.In [Go] an elegant proof by contradiction shows that a greedy algorithm will produce an interval tiling. We show that the process of converting to a direct proof leads to much stronger results.

scholarly journals Profil number sense siswa bergaya kognitif visualizer terhadap makna pecahan desimal

2018 ◽  
Vol 11 (1) ◽  
pp. 20-36
Author(s):  
Wilda Syam Tonra
Keyword(s):  
Mathematics Achievement ◽  
Cognitive Style ◽  
Number Sense ◽  
Number Line ◽  
Mathematics Tests ◽  
Basic Meaning ◽  
Decimal Fractions ◽  
The Subject ◽  
And Mathematics ◽  
Partitions Of Integers

[Bahasa]: Penelitian kualitatif ini bertujuan untuk mendeskripsikan profil number sense siswa terhadap makna pecahan desimal. Subjek penelitian adalah satu siswa kelas VII SMP Bhayangkari Kemala I Surabaya dengan kemampuan matematika tinggi dan bergaya kognitif visualizer. Penelitian dimulai dengan menentukan subjek penelitian mengunakan instrumen tes gaya kognitif dan tes kemampuan matematika, kemudian dilanjutkan dengan pemberian tes number sense (TNS). Tahap terakhir adalah melakukan wawancara dengan subjek untuk mengungkap cara berfikir siswa dalam menyelesaikan soal tes number sense serta melihat kesesuaian jawaban dengan alasan yang diberikan. Pengecekan keabsahan data dalam penelitian ini menggunakan triangulasi waktu. Hasil penelitian menunjukkan bahwa number sense yang dimiliki oleh subjek dalam memahami makna dasar pecahan desimal ditunjukkan dengan mempresentasikan pecahan desimal sebagai pecahan biasa, partisi dari bilangan bulat, dan partisi suatu benda. Pemahaman mengenai urutan pecahan desimal ditunjukkan dengan meletakkan pecahan-pecahan desimal pada garis bilangan sesuai urutan yang benar. Pemahaman mengenai sifat kerapatan pecahan desimal ditunjukkan dengan penyimpulan bahwa ada tidak hingga pecahan desimal antara dua pecahan desimal. Jadi, dapat disimpulkan bahwa siswa yang bergaya kognitif visualizer dengan kemampuan matematika tinggi dapat memahami makna pecahan desimal. Kata kunci: Number Sense; Gaya Kognitif; Visualizer; Pecahan Desimal [English]: This qualitative research aimed to describe the profile of student’s number sense toward the meaning of decimal. The research subject was one 7th grade of SMP Bhayangkari Kemala I Surabaya with high mathematics achievement and visualizer cognitive-style. The research began by determining the subject using cognitive-style test instrument and mathematics tests, then followed by the number sense test (TNS). The last stage was interviewing the subject to reveal how the subject think in solving the number sense test and examine the match between the answers and the reasons given. Time triangulation was used to check the validity of data. The research found that the number sense possessed by the subject in understanding the basic meaning of decimal is representing decimal fractions as regular fractions, partitions of integers, and partitions of an object. Understanding of the order of decimal is shown by placing the decimal on the number line in the correct order. Understanding of the nature of the decimal density is denoted by the conclusion that there are infinite decimals between two decimals. Thus, it could be concluded that students with visualizer cognitive-style and high mathematics achievement can understand the meaning of decimal properly. Keywords : Number Sense; Cognitive Style; Visualizer; Decimal

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