Challenging Problems In Algebra by Alfred S. Posamentier

By Alfred S. Posamentier

Designed for high-school scholars and academics with an curiosity in mathematical problem-solving, this stimulating assortment comprises greater than three hundred difficulties which are "off the overwhelmed direction" — i.e., difficulties that provide a brand new twist to widely used themes that introduce unusual subject matters. With few exceptions, their answer calls for little greater than a few wisdom of common algebra, although a touch of ingenuity could help.
Readers will locate right here thought-provoking posers concerning equations and inequalities, diophantine equations, quantity conception, quadratic equations, logarithms, mixtures and chance, and lots more and plenty extra. the issues diversity from relatively effortless to tough, and plenty of have extensions or diversifications the writer calls "challenges."
By learning those nonroutine difficulties, scholars won't in basic terms stimulate and advance problem-solving abilities, they're going to collect beneficial underpinnings for extra complicated paintings in mathematics.

Show description

Read Online or Download Challenging Problems In Algebra PDF

Best elementary books

How round is your circle

How do you draw a directly line? How do you identify if a circle is absolutely around? those may perhaps sound like uncomplicated or maybe trivial mathematical difficulties, yet to an engineer the solutions can suggest the variation among good fortune and failure. How around Is Your Circle? invitations readers to discover a number of the similar basic questions that operating engineers care for each day--it's difficult, hands-on, and enjoyable.

Lie Algebras and Applications

This e-book, designed for complex graduate scholars and post-graduate researchers, introduces Lie algebras and a few in their functions to the spectroscopy of molecules, atoms, nuclei and hadrons. The e-book comprises many examples that aid to explain the summary algebraic definitions. It offers a precis of many formulation of sensible curiosity, similar to the eigenvalues of Casimir operators and the scale of the representations of all classical Lie algebras.

Modern Geometries

This entire, best-selling textual content specializes in the research of many alternative geometries -- instead of a unmarried geometry -- and is carefully sleek in its strategy. each one bankruptcy is basically a brief path on one point of contemporary geometry, together with finite geometries, the geometry of changes, convexity, complicated Euclidian geometry, inversion, projective geometry, geometric elements of topology, and non-Euclidean geometries.

Additional info for Challenging Problems In Algebra

Example text

Find an equation of the plane (in R3) that contairu the points (1, 0, 0), (0, 1, 0), and {0, 0, 1). 15. The equation of a plane in R3 is 3x I 2z = 1. Give a point-normal form for this y equation. 16. A plane (in R3) has equation {2, -1, 3) equation in standard form. o ((x, )I z) - ( -1, 3, 0)) - 0. Give this 17. Find an equation of the line in R 3 that completely contains the vector v - (1, 0, 2). + t(O, 1, 0) and 18. Determine the point (in R3) of intersection of the line x(t) - (1, 0, 1) the plane x I y I z; - 0.

29. - + j 0 x1 x4"5 =3 30. Find the midpoint of the line segment that joins (2, 1, 3, 5) with (6, 3. 2, 1). 31. Prove the properties ofTheorem 2. 32. The angle bt:twt:t:n two nonuro v«tors u and v in R"' is defined to he the unique number 9, 0 :s; 8 :s; 'If radians such that cos 8 Find the cosine of the angle between the vectors (3, 1, 1, 2, 1) and (0, 2, 1, 2, 0). CIIull llvll). 33. Prove the properties ofTheorem 3. 34. Describe the plane determined by the points (3, 1, 0, 2, 1), (2, 1, 4, 2, 0), and (-1, 2, 1, 3, 1).

33. Jx2 I y 2 I c1x I CzY I c3 = 0. Suppose the points (1, 1), (0, 2), and (k, 1) lie on the same circle. Solve for the equation of the circle when k = -1, 0, 1, 2, and 3. ) For what values of k is there no solution? 34. Use a CAS or a graphing calculator to plot the points and corresponding solution for the given values of kin Exercise 33. 35. Since a CAS can perform symbolic manipulation, solve directly for the: equation of the circle: with points ( 2, 0), (1, 3), (5, k). For what value of k is there no solution?

Download PDF sample

Rated 4.43 of 5 – based on 9 votes

About admin