Fields
http://www.maa.org/taxonomy/term/41402/0
enProjective Geometry over \(F_1\) and the Gaussian Binomial Coefficients
http://www.maa.org/programs/maa-awards/writing-awards/projective-geometry-over-f1-and-the-gaussian-binomial-coefficients
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><b>Year of Award:</b> 2005</p>
<p class="MsoNormal"><b>Publication Information:</b> <i>The American Mathematical Monthly</i>, vol. 111, no. 6, June/July 2004, pp. 487-495.</p></div></div></div>Fri, 19 Sep 2008 10:02:30 +0000saratt113718 at http://www.maa.orgAn Algorithm for Multiplication in Modular Arithmetic
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-algorithm-for-multiplication-in-modular-arithmetic
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>An algorithm, with examples, for multiplying by \(m\) modulo \( \)n without actually carrying out the multiplications in ordinary arithmetic</em></p>
</div></div></div>Fri, 05 Feb 2010 15:59:52 +0000newton_admin95498 at http://www.maa.orgKirkman's Schoolgirls Wearing Hats and Walking Through Fields of Numbers
http://www.maa.org/programs/maa-awards/writing-awards/kirkmans-schoolgirls-wearing-hats-and-walking-through-fields-of-numbers
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Award: </strong>Carl B. Allendoerfer</p>
<p><strong>Year of Award:</strong> 2009</p>
<p><strong>Publication Information: </strong><em>Mathematics Magazine</em>, vol. 82, no. 1, February 2009, pp. 3-15.</p>
<p><strong>Summary:</strong> The historical basis for this interesting article is a problem in recreational mathematics posed by T. P. Kirkman in 1850.</p>
<p>"Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once."</p></div></div></div>Thu, 12 Aug 2010 12:13:38 +0000saratt114013 at http://www.maa.orgTropical Mathematics
http://www.maa.org/programs/maa-awards/writing-awards/tropical-mathematics
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Award: </strong>Carl B. Allendoerfer</p>
<p><strong>Year of Award:</strong> 2009</p>
<p><strong>Publication Information: </strong><em>Mathematics Magazine</em>, vol. 82, no. 3, June 2009, pp. 163-173.</p>
<p><strong>Summary:</strong> The adjective tropical was chosen by French mathematicians to honor Imre Simon, the Brazilian originator of min-plus algebra, which grew into this field. The basic object of study is the tropical semiring consisting of the real numbers R with a point at infinity under the operations of equals minimum and equals plus.</p></div></div></div>Thu, 12 Aug 2010 12:33:58 +0000saratt114014 at http://www.maa.orgCounting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/counting-irreducible-polynomials-over-finite-fields-using-the-inclusion-exclusion-principle
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Using just very basic knowledge of finite fields and the inclusion-exclusion formula, the authors show how one can see the shape of Gauss` formula for the number of irreducible polynomials of a given degree over a finite field .</em></p>
</div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95841 at http://www.maa.orgMatrix Representation of Finite Fields
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/matrix-representation-of-finite-fields
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The author uses matrices to represent finite fields in order to make both addition and multiplication obvious.</em></div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95641 at http://www.maa.orgWhy Study Equations over Finite Fields?
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/why-study-equations-over-finite-fields
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The article discusses the reason for studying finite fields.</em></div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95614 at http://www.maa.orgFields for Which the Principal Axis Theorem Is Valid
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/fields-for-which-the-principal-axis-theorem-is-valid
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>One version of the Principal Axis Theorem asserts that any symmetric matrix with entries in \( \mathcal{R}\) is similar over \(\mathcal{R}\) to a diagonal matrix. The authors find necessary and sufficient conditions for a field \(K\) that make the Principal Axis Theorem valid over \(K\).</em></p>
</div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95501 at http://www.maa.orgMatrices as Sums of Invertible Matrices
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/matrices-as-sums-of-invertible-matrices
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author shows that any square matrix over a field is the sum of two invertible matrices, and that the decomposition is unique only if the matrix is nonzero and of size 2x2 with entries in the field of two elements.</em></p>
</div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95464 at http://www.maa.orgUncountable Fields Have Proper Uncountable Subfields
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/uncountable-fields-have-proper-uncountable-subfields
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Does an uncountable field have any uncountable proper subfields? This paper shows the answer is "yes, always."</em></p>
</div></div></div>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95388 at http://www.maa.orgThe Existence of Multiplicative Inverse
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-existence-of-multiplicative-inverse
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the multiplicative inverse. Therefore the non-zero determinant guarantees the existence of the multiplicative inverse.</em></p>
</div></div></div>Thu, 19 Jun 2014 01:12:20 +0000lang430339 at http://www.maa.org