Number theory web american site and australian site add. Projects january 23, 2012 i chose these projects because i think they are all interesting. Karl friedrich gauss csi2101 discrete structures winter 2010. This paper considers the role of projects in teaching pure mathematics their nature and issues of using them in practice. Many problems are remained unsolved in it, which in fact the most famous and important problems are about. Topics in elementary number theory before start studying of cryptography, here is some background that shall be required.
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. Topics for an undergraduate expository paper in number theory. It must be written in latex and approximately ten pages long. 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. Explore the sequences of quadratic residues modulo m for numbers of the form mp n for p a fixed prime. The editors are grateful to springerverlag for their helpfulness and courtesy. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. What are some ideas for a research projectpaper on number.
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. Analytic number theory is indeed a very strong base in the research of number theory. I have to do a project for my number theory class undergraduate. That said, you can still do interesting problems and write them up. 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. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. Other topics in number theory mathematics libretexts. Introduction to number theory final project first details. Can you find any patterns to the number of quadratic residues or the distribution of the residues themselves. I assume you are asking for mustknow knowledge for algorithm programming contests e. I am a computer science major, so i really want a topic that relates to computing too. Scholastic teachables worksheets, lesson plans, learning games, and more. This rather unique book is a guided tour through number theory.
A valuable resource for mathematicians, the journal provides an international forum for. Each project will consist of an original treatment of important numbertheoretic material. Math 215 project number 1 graph theory and the game of. Elementary number theory projects there are going to be. Math 215 project number 1 graph theory and the game. Click and read its project contents for msc,bsc, hnd, pgd. Im not so sure if every programmer should know some number theory knowledge. 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. Rademacher started work on the present volume no later than 1944. Each student will write a paper on a topic related to the course.
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. Pdf an introduction to the theory of numbers, 6th edition. The most downloaded articles from journal of number theory in the last 90 days. 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. Divisibility, the fundamental theorem of number theory 1 1. Please do not take number theory for a collection of theories just because the word theory is literally. Algebra and number theory school of mathematics and physics. Download undergraduate projects topics and materials accounting, economics, education.
List of interesting mathematics research project topics mathematics project topics mathematics is the abstract science of number, quantity, and space, either as abstract. Explore project topics ideas for physical sciences, engineering, life sciences, health sciences, social sciences, arts, management and medical sciences on projecttopics. On potential automorphy, and other topics in number theory, phd thesis, thomas barnetlamb, harvard university 2009 on euclidean ideal classes, phd thesis, hester k. What important topics of number theory should every. It represents the parts of analytic number theory that were of greatest interest to him. Download project topics and materials, get new project topic ideas for undergraduate and masters research work. These notes serve as course notes for an undergraduate course in number the ory.
Number theory, branch of mathematics concerned with properties of the positive integers 1, 2, 3. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. 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. Each project will consist of an original treatment of important number theoretic material. Mathematics archives topics in mathematics number theory. Photograph your local culture, help wikipedia and win. Unless you choose to take a final exam, you will need to do a final project. Topics in number theory, volumes i and ii dover books on. Solutions manual elementary number theory and its applications 6th edition by kenneth h. 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. Five of the projects will have three participants and the sixth will have only two. 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.
I will nd some way of dealing with con icts, should they arise. This thesis is a presentation of my original research work. A2a as a high schooler, you likely dont have the prerequisites to do actual mathematical research. Sometimes called higher arithmetic, it is among the oldest and most natural of mathematical pursuits.
Mathematics education undergraduate project topics, research works and materials, largest undergraduate projects repository, research works and materials. Topics in mathematics number theory mathematics archives. This section contains sample student projects from the course. Reallife math project cant find what youre looking for. I will also post a pdf of the two documents to the website. 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. An introduction to the theory of numbers, 6th edition, by g. The mission of the journal is to publish highquality original articles that make a significant contribution to these research areas. These are directions and possible project topics suggested to students.
The game is called sprouts and it is an invention of john horton conway. German mathematician carl friedrich gauss 17771855 said, mathematics is the queen of the sciencesand number theory is the queen of mathematics. Are people still interested in this type of mathematics today. Some topics in number theory indian statistical institute. It is easy to see that a nonempty subset sof zis a subgroup of zif and only if x y2sfor all x2sand y2s. Use features like bookmarks, note taking and highlighting while reading topics in number theory, volumes i and ii dover books on mathematics. Bibliography of books on history of arithmetic and number theory add. Number theory has always fascinated amateurs as well as professional mathematicians. 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 is a list of number theory topics, by wikipedia page. Net, mechanicalautomobile, mba, php, embedded systems chemistry project ideas, physics thesis topics and vlsi full reports download for. This chapter discusses various topics that are of profound interest in number theory.
Michigan 2009 applications of sieve methods in analytic number theory, phd thesis, kaisa matomaki, royal holloway, university of london, 2009. Most downloaded journal of number theory articles elsevier. I am personally interested in the twin prime conjecture and prime divisibility tests and. Number theory research topics mathematics stack exchange. The journal of number theory jnt features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. Find materials for this course in the pages linked along the left.
Finally, i would like to thank amir to join me in this project. Computational number theory is also known as algorithmic number theory. The professor asked us to explore a topic from number theory and write about 5 to 10 pages on it. Download economics, education, accounting, philosophy, computer science, business administration, engineering, marketing, law project topics in. Residue number system cunningham project quadratic residuosity problem. In the course of the problems we shall also work on writing proofs that use mathematical. 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. 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. Mathematics education project topics with already well written chapters 15 content.
By undertaking a project with us, youll have the chance to create change within a range of diverse areas. 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. Wright article pdf available in contemporary physics 5. 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. Topics in the theory of numbers undergraduate texts in. 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.
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