The mission of the journal is to publish highquality original articles that make a significant contribution to these research areas. A valuable resource for mathematicians, the journal provides an international forum for. Analytic number theory is indeed a very strong base in the research of number theory. Residue number system cunningham project quadratic residuosity problem. Introduction to number theory and its applications lucia moura winter 2010 \mathematics is the queen of sciences and the theory of numbers is the queen of mathematics. Many problems are remained unsolved in it, which in fact the most famous and important problems are about. Topics in number theory, volumes i and ii dover books on. This rather unique book is a guided tour through number theory. I will also post a pdf of the two documents to the website. Each student will write a paper on a topic related to the course. Most downloaded journal of number theory articles elsevier.
German mathematician carl friedrich gauss 17771855 said, mathematics is the queen of the sciencesand number theory is the queen of mathematics. Bibliography of books on history of arithmetic and number theory add. Im not so sure if every programmer should know some number theory knowledge. This chapter discusses various topics that are of profound interest in number theory.
Download undergraduate projects topics and materials accounting, economics, education. Number theory web american site and australian site add. Projects january 23, 2012 i chose these projects because i think they are all interesting. I am teaching an undergraduate course in number theory and am looking for topics that students could take on to write an expository paper 10 pages. An introduction to the theory of numbers, 6th edition, by g. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. Introduction to number theory final project first details. Mathematics education project topics with already well written chapters 15 content.
Please do not take number theory for a collection of theories just because the word theory is literally. Number theory, software sites, computational number theory sites, conferences, courses in number theory, lecture notes, journals on a generalized fermatwiles equation add. Waclaw sierpinski 250 problems in elementary number theory presents problems and their solutions in five specific areas of this branch of mathe matics. This is a list of number theory topics, by wikipedia page. This chapter lays the foundations for our study of the theory of numbers by weaving together the themes of prime numbers, integer factorization, and the distribution of primes. Divisibility, the fundamental theorem of number theory 1 1. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. A2a as a high schooler, you likely dont have the prerequisites to do actual mathematical research. By undertaking a project with us, youll have the chance to create change within a range of diverse areas. I assume you are asking for mustknow knowledge for algorithm programming contests e. Mathematics research project topics mathematics is the abstract science of number, quantity, and space, either as abstract concepts pure mathematics or as applied to other. Pdf an introduction to the theory of numbers, 6th edition.
Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. Sometimes called higher arithmetic, it is among the oldest and most natural of mathematical pursuits. Unless you choose to take a final exam, you will need to do a final project. Elementary number theory projects there are going to be six di erent projects.
Topics in elementary number theory before start studying of cryptography, here is some background that shall be required. Five of the projects will have three participants and the sixth will have only two. The editors are grateful to springerverlag for their helpfulness and courtesy. You are free to choose which problems in this project that you would like to work on, all i ask is that you work on things which you havent seen before, and that you do not use any books or the internet. Each project will consist of an original treatment of important number theoretic material. Number theory has always fascinated amateurs as well as professional mathematicians. Download project topics and materials, get new project topic ideas for undergraduate and masters research work.
Click and read its project contents for msc,bsc, hnd, pgd. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent. I am personally interested in the twin prime conjecture and prime divisibility tests and. The journal of number theory jnt features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. The professor asked us to explore a topic from number theory and write about 5 to 10 pages on it. Are people still interested in this type of mathematics today. Topics in mathematics number theory mathematics archives. Math 215 project number 1 graph theory and the game of. What important topics of number theory should every. It is easy to see that a nonempty subset sof zis a subgroup of zif and only if x y2sfor all x2sand y2s.
Photograph your local culture, help wikipedia and win. Topics in number theory, volumes i and ii dover books on mathematics kindle edition by leveque, william j download it once and read it on your kindle device, pc, phones or tablets. Math 215 project number 1 graph theory and the game. Number theory or arithmetic or higher arithmetic in older usage is a branch of pure mathematics devoted primarily to the study of the integers and integervalued functions. Elementary number theory projects there are going to be. Huge list of project topics or ideas 2017, base papers, source code, reports, ppt, abstracts, synopsis, pdf, doc thesis, dissertation for ieee electrical, electronics and telecommunication, computer science, mca, information technology, java application. The game is called sprouts and it is an invention of john horton conway. Students were asked to choose a serious topic in number theory of which the projects were my suggestions with useful references to write a final paper of at least 10 pages explaining their topic i. I am a computer science major, so i really want a topic that relates to computing too. List of interesting mathematics research project topics mathematics project topics mathematics is the abstract science of number, quantity, and space, either as abstract. Section 1 on cryptography is on an application of number theory in the field of message decoding, while the other sections on elliptic curves and the riemann zeta function are deeply connected with number theory. Other topics in number theory mathematics libretexts.
Mathematics education undergraduate project topics, research works and materials, largest undergraduate projects repository, research works and materials. In the course of the problems we shall also work on writing proofs that use mathematical. Huge list of mathematics projectsproject topics, mathematics projects, 2015 latest mathematics science fair project ideas, maths topics gcse cbse,mathematics lab, additional project work, maths model project ideas for cbse high school, cool easy experiments for kids and also for middle school, elementary school for class 5th grade, 6th, 7th, 8th, 9th, 10th, 11th, 12th grade and high school. Topics in the theory of numbers undergraduate texts in. That said, you can still do interesting problems and write them up.
The most downloaded articles from journal of number theory in the last 90 days. This thesis is a presentation of my original research work. Mathematics archives topics in mathematics number theory. I will nd some way of dealing with con icts, should they arise. It must be written in latex and approximately ten pages long. Math 215 project number 1 graph theory and the game of sprouts this project introduces you to some aspects of graph theory via a game played by drawing graphs on a sheet of paper. Topics for an undergraduate expository paper in number theory. Some typical number theoretic questions the main goal of number theory is to discover interesting and unexpected relationships between different sorts of numbers and to prove that these relationships are true. This paper considers the role of projects in teaching pure mathematics their nature and issues of using them in practice. Mathematics free undergraduate project topics and research materials, free undergraduate project topics, research materials, education project topics, economics project topics, computer science project topics, hire a data analyst. Michigan 2009 applications of sieve methods in analytic number theory, phd thesis, kaisa matomaki, royal holloway, university of london, 2009. Find materials for this course in the pages linked along the left.
On potential automorphy, and other topics in number theory, phd thesis, thomas barnetlamb, harvard university 2009 on euclidean ideal classes, phd thesis, hester k. Computational number theory is also known as algorithmic number theory. This section contains sample student projects from the course. Pdf two topics in number theory a formula for primes and an. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Finally, i would like to thank amir to join me in this project. Number theory research topics mathematics stack exchange. Can you find any patterns to the number of quadratic residues or the distribution of the residues themselves.
Karl friedrich gauss csi2101 discrete structures winter 2010. Net, mechanicalautomobile, mba, php, embedded systems chemistry project ideas, physics thesis topics and vlsi full reports download for. Use features like bookmarks, note taking and highlighting while reading topics in number theory, volumes i and ii dover books on mathematics. Number theory, branch of mathematics concerned with properties of the positive integers 1, 2, 3. These notes serve as course notes for an undergraduate course in number the ory. I have to do a project for my number theory class undergraduate. Reallife math project cant find what youre looking for. Rademacher started work on the present volume no later than 1944. Explore project topics ideas for physical sciences, engineering, life sciences, health sciences, social sciences, arts, management and medical sciences on projecttopics. Wright article pdf available in contemporary physics 5. Download economics, education, accounting, philosophy, computer science, business administration, engineering, marketing, law project topics in. Scholastic teachables worksheets, lesson plans, learning games, and more. Each project will consist of an original treatment of important numbertheoretic material. Solutions manual elementary number theory and its applications 6th edition by kenneth h.
Some topics in number theory indian statistical institute. Algebra and number theory school of mathematics and physics. Explore the sequences of quadratic residues modulo m for numbers of the form mp n for p a fixed prime. It represents the parts of analytic number theory that were of greatest interest to him. What are some ideas for a research projectpaper on number.
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