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Primality Testing for Beginners

How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.

are common (e.g., in English, “e” and “t”, or “th” and “he”) and can try to find these
in the ciphertext. The more encrypted messages we have intercepted, the better
this methods works since the probability rises that letters will really be distributed
 ...

English Language Learners and Math

Discourse, Participation, and Community in Reform-oriented, Middle School Mathematics Classes

Taking a community of practice perspective that highlights the learner as part of a community, rather than a lone individual responsible for her/his learning, this ethnographically-influenced study investigates how Latina/o English Language Learners (ELLs) in middle school mathematics classes negotiated their learning of mathematics and mathematical discourse. The classes in which the Latina/o students were enrolled used a reform-oriented approach to math learning; the math in these classes was-to varying degrees-taught using a hands-on, discovery approach to learning where group learning was valued, and discussions in and about math were critical. This book presents the stories of how six immigrant and American-born ELLs worked with their three teachers of varied ethnicity, education, experience with second language learners, and training in reform-oriented mathematics curricula to gain a degree of competence in the mathematical discourse they used in class. Identity, participation, situated learning, discourse use by learners of English as a Second Language (ESL), framing in language, and student success in mathematics are all critical notions that are highlighted within this school-based research.

This book presents the stories of how six immigrant and American-born ELLs worked with their three teachers of varied ethnicity, education, experience with second language learners, and training in reform-oriented mathematics curricula to ...

A Grammar of English on Mathematical Princibles

For the precise derivation we start with One (or Someone) is in math- teaching
where math-teaching is reduced from teaching of math by one, which is
nominalized from One teaches math (5.25). We then form: He is one (or: a person
); said one ...

Russian-English Mathematical Dictionary

Words and Phrases in Pure and Applied Mathematics with Roots and Accents, Arranged for Easy Reference

Proposed Problems of Mathematics, Vol. II, Second edition - entirely translated to English

Mathematical problems for student competitions, translated from Romanian and French into English.

Florentin Smarandache. Remarks This problem is valid for a non-constant
geometrical progression too. (see [1], p.69). It is a generalization of the Problem 5
, Mathematics International Olympiad, Paris, 1983; (When ...

Dasar-Dasar Aljabar Linear dan Penggunaannya dalam Berbagai Bidang

Sebagai salah satu cabang matematika, aljabar linear banyak dipakai di berbagai bidang lainnya, baik teori maupun terapannya. Secara umum, mahasiswa Matematika, Statistika, Ilmu Komputer, dan Teknik di hampir semua perguruan tinggi wajib mengetahui dan menguasai aljabar linear. Untuk lebih menunjang proses pembelajaran aljabar linear, disusunlah buku ini yang merupakan pengembangan dan penyempurnaan pengalaman mengajar oleh penulis di kelas dan diktat yang sudah ada. Selain teori, buku ini juga mengangkat beberapa penerapan aljabar linear elementer pada bidang-bidang tertentu. Keterangan dan penjelasan yang melengkapi contoh dan ilustrasi sangat diperlukan agar buku ini menjadi semakin mudah dipahami oleh pembaca. Teori yang dibahas dalam buku ini menjadi landasan untuk memahami aljabar linear lebih lanjut, baik yang bersifat terapan maupun abstrak. Dengan pemikiran tersebut, isi buku ini dibuat menggunakan pendekatan pembelajaran berbasis riset.

Sebagai salah satu cabang matematika, aljabar linear banyak dipakai di berbagai bidang lainnya, baik teori maupun terapannya.

Russian-English Dictionary of Mathematics

An essential book for anyone using Russian mathematical and scientific literature Russian-English Dictionary of Mathematics embraces all major branches of mathematics from elementary topics to advanced studies in topology and discrete mathematics. Terms from the newest branches of mathematics, such as the theories of games, trees, knots, and braids, are included as well.Containing more than 27,000 entries, Russian-English Dictionary of Mathematics is larger and provides a broader scope than any other bilingual mathematics dictionary now in use. Many adjectives and verbs are included, and a copious amount of synonyms are provided for various terms. Secondary terms are grouped under principal terms for easier reference.Russian-English Dictionary of Mathematics provides the most comprehensive vocabulary aid available for translators, readers, and writers of Russian mathematical and scientific literature.

An essential book for anyone using Russian mathematical and scientific literature Russian-English Dictionary of Mathematics embraces all major branches of mathematics from elementary topics to advanced studies in topology and discrete ...

Linear Programming

Methods and Applications

Comprehensive, well-organized volume, suitable for undergraduates, covers theoretical, computational, and applied areas in linear programming. Expanded, updated edition; useful both as a text and as a reference book. 1995 edition.

Tomlin [648] notes that the _reasons for scaling linear-programming problems
are (a) to make all variables with a finite upper bound have the same bound, e.g.,
all have unit upper bounds (see Orchard-Hays [532]), (b) to reduce the number of
 ...

Linear Programming with MATLAB

A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required.

In this chapter, we consider some extensions of linear programming to other
mathematical programming problems. We first look at nonlinear problems,
deriving optimality conditions based solely on calculus arguments and convexity
properties ...