Topics in Algebra

@inproceedings{Newman1978TopicsIA,
  title={Topics in Algebra},
  author={Mike F. Newman and J. S. Richardson},
  year={1978}
}
• Review signed numbers and arithmetic operations • Review fractions, decimals and percents • Order of Operations • Number sense • Properties of real numbers • The coordinate plane • Graphing linear equations • Graphing linear inequalities • Slope • Finding the equation of a line • Solving linear equations and inequalities and their applications • Solving Systems of Linear Equations and Inequalities (2 equations with 2 unknowns) by graphing and analytically and application problems • Absolute… 
COMPOSITION SERIES OF THE SOLVABLE ABELIAN FACTOR GROUP SOURCE OF EQUATION OF ALL POLYNOMIAL EQUATIONS
This work penciled down the Composition Series of Factor Abelian Group over the source of all polynomial equations gleaned through  the nth roots of unity regular gons on a unit circle, a circle of
Commutativity theorems: examples in search of algorithms
TLDR
This paper presents several examples of commutativity theorems with solutions that were obtained using a reduction process for non-commutative polynomials with integer coefficients.
Computer Algebra and Symbolic Computation: Mathematical Methods
TLDR
Maintaining the style set by Elementary Algorithms, the author explains mathematical methods as needed while introducing advanced methods to treat complex operations.
Computer Discovery and Analysis of Large Poisson Polynomials
TLDR
This study addresses the Poisson polynomial problem with significantly more capable computational tools and confirms that Kimberley’s formula holds for all integers s up to 52, and also for s = 60 and s = 64.
The Greedy Algorithm and the Cohen-Macaulay Property of Rings, Graphs and Toric Projective Curves
It is shown in this paper how a solution for a combinatorial problem obtained from applying the greedy algorithm is guaranteed to be optimal for those instances of the problem that, under an
The basis of a computer system for modern algebra
TLDR
So-called general purpose systems for algebraic computation such as ALTRAN, MACSYMA, SAC, SCRATCHPAD and REDUCE are designed to compute with elements in a fixed algebraic structure and provide some operations from calculus: differentiation, integration, the calculation of limits, and the analytic solution of certain classes of differential equations.
A Geometric Interpretation of the Solution of the General Quartic Polynomial
where each of the ai's is a rational number and a, is not zero. We might ask if the solutions of this equation can be expressed in terms of the coefficients aO, . . ., a, using only the operations of
Efficient variable elimination using resultants
TLDR
A new method for eliminating variables from polynomial equations is proposed, analyzed, evaluated and applied and it is proved that for most classes of polynomials systems, the proposed method is more efficient than other prevalent resultant algorithms.
Why the nth-root function is not a rational function
ABSTRACT The set of functions is linearly independent over (with respect to any open subinterval of (0, ∞)). The titular result is a corollary for any integer n ≥ 2 (and the domain [0, ∞)). Some more
Computing automorphisms of finite soluble groups
  • Michael J. Smith
  • Mathematics, Computer Science
    Bulletin of the Australian Mathematical Society
  • 1996
TLDR
In this thesis an algorithm for computing the automorphism group of a finite soluble group is described and the effectiveness of the algorithm is demonstrated by performance results for a prototype implementation.
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