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Barnard S

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Open University

Higher Algebra

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

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Classics

Barnard Press

HIGHER ALGEBRA by S. BARNARD. First published in 1936. Contents include: ix CHAPTER EXERCISE XV ( 128). Minors, Expansion in Terms of Second Minors ( 132, 133). Product of Two Iteterminants ( 134). Rectangular Arrays ( 135). Reciprocal Deteyrrtlilnts, Two Methods of Expansion ( 136, 137). Use of Double Suffix, Symmetric and Skew-symmetric Determinants, Pfaffian ( 138-143), EXERCISE XVI ( 143) X. SYSTEMS OF EQUATIONS. Definitions, Equivalent Systems ( 149, 150). Linear Equations in Two Unknowns, Line at Infinity ( 150-152). Linear Equations in Three Unknowns, Equation to a Plane, Plane at Infinity ( 153-157). EXERCISE XVII ( 158). Systems of Equations of any Degree, Methods of Solution for Special Types ( 160-164). EXERCISE XVIII ( 164). XL RECIPROCAL AND BINOMIAL EQUATIONS. Reduction of Reciprocal Equations ( 168-170). The Equation x n - 1= 0, Special Roots ( 170, 171). The Equation x n - A = 0 ( 172). The Equation a 17 - 1 == 0, Regular 17-sided Polygon ( 173-176). EXERCISE XIX ( 177). AND BIQUADRATIC EQUATIONS. The Cubic Equation ( roots a, jS, y), Equation whose Roots are ( - y) 2 , etc., Value of J, Character of Roots ( 179, 180). Cardan's Solution, Trigonometrical Solution, the Functions a - f eo/? - f-\> V> a-f a> 2 4-a> y ( 180, 181). Cubic as Sum of Two Cubes, the Hessftfh ( 182, 183). Tschirnhausen's Transformation ( 186). EXERCISE XX ( 184). The Biquadratic Equation ( roots a, , y, 8) ( 186). The Functions A= y + aS, etc., the Functions /, J, J, Reducing Cubic, Character of Roots ( 187-189). Ferrari's Solution and Deductions ( 189-191). Descartes' Solution ( 191). Conditions for Four Real Roots ( 192-ty). Transformation into Reciprocal Form ( 194). Tschirnhausen's Trans formation ( 195). EXERCISE XXI ( 197). OP IRRATIONALS. Sections of the System of Rationals, Dedekind's Definition ( 200, 201). Equality and Inequality ( 202). Use of Sequences in defining a Real Number, Endless Decimals ( 203, 204). The Fundamental Operations of Arithmetic, Powers, Roots and Surds ( 204-209). Irrational Indices, Logarithms ( 209, 210). Definitions, Interval, Steadily Increasing Functions ( 210). Sections of the System of^ Real Numbers, the Continuum ( 211, 212). Ratio and Proportion, Euclid's Definition ( 212, 213). EXERCISE XXII ( 214). x CONTENTS CHAPTER XIV/ INEQUALITIES. Weierstrass' Inequalities ( 216). Elementary Methods ( 210, 217) For n Numbers a l9 a 2 a > \* JACJJ n n n ( a* -!)/* ( a - I)/*,, ( 219). xa x ~ l ( a-b)$ a x - b x ^ xb x ~ l ( a - 6), ( 219). ( l+ x) n ^ l+ nx, ( 220). Arithmetic and Geometric Means ( 221, 222). - - V ^ n and Extension ( 223). Maxima and Minima ( 223, 224). EXERCISE XXIII ( 224). XV. SEQUENCES AND LIMITS. Definitions, Theorems, Monotone Sequences ( 228-232). E* ponential Inequalities and Limits, l\ m / i\ n / l\-m / 1 \ ~ n 1) >(!+-) and ( 1--)  n, m/ \ n/ \ mj \ nj / 1 \ n / l\ w lim ( 1-f-= lim( l--) = e, ( 232,233). n _ > 00 V nj \ nj EXERCISE XXIV ( 233). General Principle of Convergence ( 235-237). Bounds of a Sequent Limits of Inde termination ( 237-240). Theorems : ( 1) Increasing Sequence ( u n ), where u n - u n ^ l < k( u n _^\^ n _ z ^ 1 ( 2) If u n > 0 and u n+ l lu n -* l, then u n n -* L ( 3) If lim u n l, then lim ( U

Science & Math

Mathematics

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<p>This textbook of Algebra is essentially for junior college and college students preparing for Science and Engineering courses. The treatise introduces the core higher algebraic concepts such as complex numbers, theory of equations, determinants, sequences and limits, etc. to equip students with mathematical acumen to move to the higher levels. The chapters are arranged in line with the reasoning followed by the authors, expecting the students to follow it.</p>

Child, J. M.

New Age Intl Uk Ltd

<p>This book contains all elements (including the parallel postulate and the axioms) and the basic propositions of geometry. Details of Euclid's definitions and its adaptation to explain various geometries have been attempted thoroughly.</p>

Elements of Geometry

New Academic Science

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Books by Barnard S