Algebra & geometry: an introduction to university by Mark V. Lawson

By Mark V. Lawson

Algebra & Geometry: An advent to school arithmetic presents a bridge among highschool and undergraduate arithmetic classes on algebra and geometry. the writer exhibits scholars how arithmetic is greater than a set of tools through offering very important rules and their old origins in the course of the textual content. He encompasses a hands-on method of proofs and connects algebra and geometry to varied functions. The textual content specializes in linear equations, polynomial equations, and quadratic varieties. the 1st numerous chapters hide foundational subject matters, together with the significance of proofs and houses more often than not encountered while learning algebra. the rest chapters shape the mathematical middle of the e-book. those chapters clarify the answer of other different types of algebraic equations, the character of the options, and the interaction among geometry and algebra

Show description

Read Online or Download Algebra & geometry: an introduction to university mathematics PDF

Similar geometry books

Geometry II (Universitext)

This can be the second one a part of the 2-volume textbook Geometry which supplies a truly readable and vigorous presentation of huge elements of geometry within the classical feel. an enticing attribute of the booklet is that it appeals systematically to the reader's instinct and imaginative and prescient, and illustrates the mathematical textual content with many figures.

The Works of Archimedes (Dover Books on Mathematics)

Whole works of historic geometer in hugely obtainable translation by means of unusual student. themes comprise the well-known difficulties of the ratio of the components of a cylinder and an inscribed sphere; the size of a circle; the homes of conoids, spheroids, and spirals; and the quadrature of the parabola.

Geometry (Idiot's Guides)

On the subject of every person takes a geometry type at one time or one other. And whereas a few humans speedy seize the techniques, so much locate geometry hard. masking every thing one might count on to come across in a highschool or university path, Idiot's courses: Geometry covers every little thing a pupil would have to comprehend.

The Special Theory of Relativity: A Mathematical Approach

The booklet expounds the most important subject matters within the exact conception of relativity. It offers a close exam of the mathematical beginning of the distinct conception of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. in addition to covariant formula of relativistic mechanics and electrodynamics, the publication discusses the relativistic influence on photons.

Extra info for Algebra & geometry: an introduction to university mathematics

Sample text

There is no reason to stop at cubes; we could likewise try to find the whole number solutions to x4+y4=z4 or more generally xn+yn=zn where n蠅3. Excluding the trivial case where xyz=0, the question is to find all the whole number solutions to equations of the form xn+yn=zn for all n蠅3. Back in the seventeenth century, Fermat, whom we met earlier, wrote in the margin of his copy of the Arithmetica, that he had found a proof that there were no solutions to these equations but that there was no room for him to write it out.

A proof shows that a result is true. A proof is something that you can follow for yourself and at the end you will see the truth of what has been proved. A result that has been proved to be true is called a theorem. The remainder of this chapter is devoted to an introductory answer to the question of what a proof is. 2膔FUNDAMENTAL ASSUMPTIONS OF LOGIC In order to understand how proofs work, three simple assumptions are needed. Mathematics only deals in statements that are capable of being either true or false.

Exclude the case where c=0 since then a=0 and b=0. We can therefore divide both sides by c2 to get (ac)2+(bc)2=1. Recall that a rational number is a real number that can be written in the form uv where u and v are whole numbers and v蠀0. It follows that (x,y)=(ac,bc) is a point with rational coordinates that lies on the unit circle, what we call a rational point. Thus Pythagorean triples give rise to rational points on the unit circle. We now go in the opposite direction. Suppose that (x,y)=(mn,pq) is a rational point on the unit circle.

Download PDF sample

Rated 4.33 of 5 – based on 19 votes