A research project can be a very important part of an education inmathematics. High school and college students often have trouble finding appropriate topics for research projects in mathematics. These sources do not list project topics! but they present a wealth of mathematical subjects in an accessible way.

The math forum website posts problems of the week in geometry, algebra, discrete math, trig amp calculus. The site also links to problems of the week administered by others, including the challenging college level problems of macalester college, the interactive escot problem of the week, and several team based projects. Joe malkevitch 39 s math stories in the feature column introduce areas of mathematical exploration. This list is a copy of the list possible science fair mathematics projects which was created by afton h.

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what 39 s happening in the mathematical sciences is a series of publications from the ams and can be ordered from the ams bookstore. Each issue has 10 or more articles by a science writer, covering a new development in the mathematical sciences. Subjects treated are on the frontiers of mathematical research,but reading about them can be useful in searching for an area to explore. Joseph malkevitch of york college, cuny, maintains the web page mathematical research for high school students.

+plus magazine is a monthly web publication, part of the millenium mathematics project sponsored by the university of cambridge and cambridge university press. Every month there are 5 or 6 very accessible articles onmathematical topics along with puzzles and news. The two core articles in this web are are: descriptive mathematics and the calculus in perspective.

They treat the study of mathematics as a series of increasingly complex problems. Unfortunately, this approach gives students an unbalanced view of the subject, and has the negative effect of alienating those students whose verbal skills are stronger than their problem solving skills. In this work, i concentrate on how to use mathematics to create and describe complex mathematical models. The goal of descriptive mathematics is to help students develop the ability to explore and discuss issues using mathematical models. This method encourages students to develop a strong mathematical vocabulary in conjunction with their problem solving skills. Students who study descriptive mathematics should not only be able to solve problems, but should be able to express their ideas. the calculus in perspective is a prime example of how i would use descriptive mathematics to develop a math class.

I begin by creating a model of visual perspective, then expand this model into a larger theory of the calculus. Perspective gives the students the skills needed to project a three dimensional shape onto a two dimensional surface. To avoid the philosophical problems inherent in the use of limits, infinitesimals and other infinite constructs, i have chosen to present the fundamental theorem of the calculus with simple primary school algebra. By avoiding the complexities of the infinite, i believe that we will be able to teach students the vocabulary of the calculus at an earlier age. My ultimate hope would be for students to learn the basic model of calculus in junior high school, or high school at the latest, then to take a rigorous two year course in calculus in their first years of college.

This work is substantially easy to comprehend than the standard two year college course. Students should be able to read this work if they know to following: how to describe a line with an equation, how to chart a graph on the cartesian plane, how to solve a binomial y ax 2 c using either the quadratic equation, or by completing the square. Although this work is easier to master than the standard college level course in calculus, i would not recommend using it as a replacement of the rigorous two year study of the cauchy method taught in most colleges. There are some very important things that students should learn about function theory, limits, and solving complex differential equations.

However, reading through this web site before taking a college level course will make the course more enjoyable. Most importantly, studying the calculus in perspective is better than never taking calculus at all. Unfortunately my work, the calculus in perspective, has pulled me head long into the debate about the nature of the calculus. In my work, i view the calculus as a model that is independent of the tools used to derive the model. Limits, infinitesimals, and standard high school algebra are all valid tools for exploring the calculus.

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Best Thesis Topics for Psychology

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