Number Theory Through Inquiry

Number Theory Through Inquiry
Author: David C. Marshall
Publisher: American Mathematical Soc.
Total Pages: 140
Release: 2020-08-21
Genre: Education
ISBN: 1470461595

Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

Number Theory

Number Theory
Author: George E. Andrews
Publisher: Courier Corporation
Total Pages: 292
Release: 2012-04-30
Genre: Mathematics
ISBN: 0486135101

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Discovering Group Theory

Discovering Group Theory
Author: Tony Barnard
Publisher: CRC Press
Total Pages: 286
Release: 2016-12-19
Genre: Mathematics
ISBN: 1315405768

Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.

Biscuits of Number Theory

Biscuits of Number Theory
Author: Arthur T. Benjamin
Publisher: American Mathematical Soc.
Total Pages: 331
Release: 2020-07-29
Genre: Mathematics
ISBN: 1470458438

An anthology of articles designed to supplement a first course in number theory.

Number Theory

Number Theory
Author: Andrej Dujella
Publisher:
Total Pages: 636
Release: 2021
Genre:
ISBN: 9789530308978

Discovering Number Theory

Discovering Number Theory
Author: Jeffrey J. Holt
Publisher: W H Freeman & Company
Total Pages: 649
Release: 2001
Genre: Mathematics
ISBN: 9780716742845

As the title suggests, Discovering Number Theory encourages students to figure out many of the important concepts and theorems of number theory for themselves. With the help of interactive computer software, students work on research questions before being exposed to the final polished theorems and proofs. By actively participating in the development of course topics they develop a solid understanding of the material and gain valuable insights into the realities of mathematical research.

Discovering Modern Set Theory. I: The Basics

Discovering Modern Set Theory. I: The Basics
Author: Winfried Just
Publisher: American Mathematical Soc.
Total Pages: 230
Release: 1996
Genre: Mathematics
ISBN: 0821802666

This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

Disquisitiones Arithmeticae

Disquisitiones Arithmeticae
Author: Carl Friedrich Gauss
Publisher: Springer
Total Pages: 491
Release: 2018-02-07
Genre: Mathematics
ISBN: 1493975609

Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .

Topics in Number Theory

Topics in Number Theory
Author: Basil Gordon
Publisher: Springer Science & Business Media
Total Pages: 280
Release: 1999-03-31
Genre: Computers
ISBN: 9780792355830

This volume contains the proceedings of the Topics in Number Theory Conference held at the Pennsylvania State University from July 31 through August 3, 1997. It contains seventeen research papers covering many areas of number theory; among them are contributions from four of the eight plenary speakers

Number Theory for Beginners

Number Theory for Beginners
Author: Andre Weil
Publisher: Springer Science & Business Media
Total Pages: 72
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461299578

In the summer quarter of 1949, I taught a ten-weeks introductory course on number theory at the University of Chicago; it was announced in the catalogue as "Alge bra 251". What made it possible, in the form which I had planned for it, was the fact that Max Rosenlicht, now of the University of California at Berkeley, was then my assistant. According to his recollection, "this was the first and last time, in the his tory of the Chicago department of mathematics, that an assistant worked for his salary". The course consisted of two lectures a week, supplemented by a weekly "laboratory period" where students were given exercises which they were. asked to solve under Max's supervision and (when necessary) with his help. This idea was borrowed from the "Praktikum" of German universi ties. Being alien to the local tradition, it did not work out as well as I had hoped, and student attendance at the problem sessions so on became desultory. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. Rather than a literal reproduction of the course, they should be regarded as its skeleton; they were supplemented by references to stan dard text-books on algebra. Max also contributed by far the larger part of the exercises. None of ,this was meant for publication.