Mathematics

Technical Reports

2023

• "My Take: Proof Research at the Undergraduate Level--How it Has Evolved", Annie Selden, New Mexico State University. Tech Report No. 2023-1, downloadable file 454 KB

2018

• "A Presentation on a Construction of Real Numbers", Courtney Riggs, Tennessee Tech University, Tech Report No. 2018-3, downloadable file 306 KB
• "Singular Value Decomposition", Andrew Lounsbury, Tennessee Tech University, Tech Report No. 2018-2, downloadable file 2,544 KB
• "Spinor Modules of Clifford Algebras in Classes N_(2k-1) and Omega_(2k-1) are Determined by Irreducible Nonlinear Characters of Corresponding Salingaros Vee Groups", Rafal Ablamowicz, Tennessee Tech University, Tech Report No. 2018-1, downloadable file 470 KB

2017

• "A Classification of Clifford Algebras as Images of Group Algebras of Salingaros Vee Groups", Rafal Ablamowicz, Manisha Varahagiri and Anne Marie Walley, Tennessee Tech University, Tech Report No. 2017-3, downloadable file 577 KB
• "40+ Years of Teaching and Thinking About University Mathematics Students, Proofs, And Proving: An Abbreviated Academic Memoir", Annie Selden, New Mexico State University. Tech Report No. 2017-2, downloadable file 938 KB
• "Alice Slowly Develops Self-Efficacy with Writing Proof Frameworks, but Her Initial Progress and Sense of Self-Efficacy Evaporates When She Encounters Unfamiliar Concepts: However, It Eventually Returns", Ahmed Benkhalti, Annie Selden and John Selden, New Mexico State University. Tech Report No. 2017-1, downloadable file 783 KB

2016

• "Graded Clifford Algebras and Graded Skew Clifford Algebras: A Survey of the Role of These Algebras in the Classification of Artin-Schelter Regular Algebras", Padmini Veerapen, Tennessee Tech University, Tech Report No. 2016-4, downloadable file 318 KB
• "On the Structure Theorem of Clifford Algebras", Rafal Ablamowicz, Tennessee Tech University, Tech Report No. 2016-3, downloadable file 165 KB
• "On Clifford Algebras and the Related Finite Groups and Group Algebras", Rafal Ablamowicz, Tennessee Tech University, Tech Report No. 2016-2, downloadable file 241 KB
• "Proof Frameworks - A Way To Get Started", Annie Selden, Professor Emerita of Mathematics from Tennessee Technological University and currently Adjunct Professor of Mathematics at New Mexico State University. John Selden taught at Tennessee Technological University and is now Adjunct Professor of Mathematics at New Mexico State University. Ahmed Benkhalti is an interdisciplinary PhD student in mathematics and education at New Mexico State University. Tech Report No. 2016-1, downloadable file 889KB

2015

• "Steinhaus Property in Banach Lattices", Damian Kubiak and David Tidwell, Tennessee Tech University, Tech Report No. 2015-1, downloadable file 254 KB
• "Groebner Bases in Teaching Computational Methods in Engineering", Y. Jane Liu, Civil and Environmental Engineering, and Rafal Ablamowicz, Department of Mathematics, Tennessee Tech University, Tech Report No. 2015 2, downloadable file 168 KB
• "Representations and Characters of Salingaros' Vee Groups of Low Order", K. D. Gayan Maduranga, Department of Mathematics, University of Kentucky, and Rafal Ablamowicz, Department of Mathematics, Tennessee Tech University, Tech Report No. 2015-3, downloadable file 245 KB
• "Validation of Proofs as a Type of Reading and Sense-Making: Illustrated by an Empirical Study", Dr. Annie Selden and Dr. John Selden, New Mexico State University, Tech Report No. 2015-4, downloadable file 417 KB

2014

• "An Elementary Introduction to Schatten Classes", Hieu Pham, Tennessee Tech University, Tech Report No. 2014-1, downloadable file 309 KB

2013

• "The Genre of Proof", Annie Selden, and John Selden, New Mexico State University, Tech Report No. 2013-1, downloadable file 503 KB
• "Bilinear Covariants and Spinor Field Classification in Quantum Clifford Algebras", Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, Icaro Gonclaves, and Roldao Da Rocha, Centro de Matematica, Computacao e Congnicao, Universidade Federal do ABC, Tech Report No. 2013-2, downloadable file 192 KB
• "The Importance of, and the Need for, Research on How Students Read and Use their Mathematics Textbooks", Annie Selden, New Mexico State University, and Mary D. Shepherd, Northwest Missouri State University, Tech Report No. 2013-3, downloadable file 224 KB
• "Rings of Invariants for Salingaros' Vee Groups", Aravwla Mudalige Dona Madhusha Shadini, Department of Mathematics, Tennessee Tech, Tech Report No. 2013-4, downloadable file 100KB

2012

• "Using Periodicity Theorems for Computations in Higher Dimensional Clifford Algebras", Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, and Bertfried Fauser, School of Computer Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2012-1, downloadable file 167KB
• "On Parallelizing The Clifford Algebra Product for Clifford", Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, and Bertfried Fauser, School of Computer Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2012-2, downloadable file 124 KB
• "Square Roots of -1 in Real Clifford Algebras", Eckhard Hitzer,Department of Applied Physics, University of Fukui, Japan, Jacques Helmstetter, Universite Greauble I, Institut Fourier Mathematiques, France, and Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, Tech Report No. 2012-3, downloadable file 378.42 KB
• "Homeomorphisms on a Cantor Set with Subsequentially Dense Orbits", Andrzej Gutek, Department of Mathematics, Tennessee Tech, Tech Report No. 2012-4, downloadable file 263 KB
• "Text Revelance and Learning from One's Undergraduate Mathematics Textbook", Annie Selden, New Mexico State University, and Mary D. Shepherd, Department of Mathematics, Northwest Missouri State University, Tech Report No. 2012-5, downloadable file 342 KB
• "A Home for RUME: The Story of the Formation of the Mathematical Association of America's Special Interest Group of Research in Mathematical Education", Annie Selden, New Mexico State University, Tech Report No. 2012-6, downloadable file 690KB

2011

• "Transposition Anti-Involution in Clifford Algebras and Invariance Groups of Scalar Products on Spinor Spaces" , Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, and Bertfried Fauser, School of Computer Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2011-3, downloadable file 224 KB
• " Possible Reasons for Students' Ineffective Reading of their First-Year University Mathematics Textbook", Mary D. Shepherd, Department of Mathematics, Northwest Missouri State University, Annie Selden, New Mexico State University, and John Selden, New Mexico State University, Tech Report No. 2011-2, downloadable file, 8.36MB
• "On the Transposition Anti-Involution in Real Clifford Algebras III: The Automorphism Group of The Transposition Scalar Product on Spinor Spaces", Rafal Ablamowicz, Department of Mathematics, Tennessee Tech, and Bertfried Fauser, School of Compter Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2011-1, downloadable file, 296KB

2010

• "Transitions and Proof and Proving at Tertiary Level", Annie Selden, Department of Mathematics, New Mexico State University, Tech Report No. 2010-3, downloadable file, 269KB
• "On the Transposition Anti-Involution in Real Clifford Algebras I: The Transposition Map" , Rafal Ablamowicz, Department of Mathematics Tennessee Tech, and Bertfried Fauser, School of Computer Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2010-1, downloadable file, 360KB
• "On the Transposition Anti-Involution in Real Clifford Algebras II: Stabilizer Groups of Primitive Idempotents" Rafal Ablamowicz, Department of Mathematics Tennessee Tech, and Bertfried Fauser, School of Computer Science, The University of Birmingham, Edgbaston-Birmingham, Tech Report No. 2010-2, downloadable file, 340KB

2009

• "Affect, Behavioral Schemas, and the Proving Process", Annie Selden, Kerry McKee, and John Selden, Department of Mathematics, New Mexico State University, Tech Report No. 2009-5, downloadable file, 135KB
• "Computations with Clifford and Grassmann Algebras", Rafal Ablamowicz, Department of Mathematics Tennessee Tech, Tech Report No. 2009-4, downloadable file, 412KB
• "Geometric Roots of -1 in Clifford Algebras Cl p,q with p + q ≤ 4", Eckhard Hitzer, Department of Applied Physics, University of Fukui, Japan, and Rafal Ablamowicz, Department of Mathematics Tennessee Tech, Tech Report No. 2009-3, downloadable file, 296KB
• "Schur Polynomials and the Irreducible Representations of Sn ", Sheela Brachey, Department of Mathematics Tennessee Tech, Tech Report No. 2009-2, downloadable file, 245KB
• "Difficulties First-year University Students Have in Reading Their Mathematics Textbooks", Mary D. Shepherd, Department of Mathematics Northwest Missouri State University, Annie Selden, New Mexico State University and John Selden, New Mexico State University, Tech Report No. 2009-1, March 2009, **downloadable file, 8,600KB,.pdf(file too big)

2008

• "Gröbner Bases Algorithms for Grassmann Algebras in a Maple Package", Troy Brachey, Department of Mathematics Tennessee Tech, Tech. Report No. 2008-1, October 2008, downloadable file, 204KB
• "Computation of Non-Commutative Gröbner Bases in Grassmann and Clifford Algebras", Rafal Ablamowicz, Department of Mathematics Tennessee Tech, Tech. Report No. 2008-2, December 2008, downloadable file, 364KB
• "Some Applications of Gröbner Bases in Robotics and Engineering", Rafal Ablamowicz, Department of Mathematics Tennessee Tech, Tech. Report No. 2008-3, December 2008, downloadable file, 823KB

2007

• "Teaching Proving by Coordinating Aspects of Proofs with Students' Abilities¹", Annie and John Selden, New Mexico State University, Tech. Report No. 2007-2, October 2007, downloadable file, 421KB
• "Overcoming Students' Difficulties in Learning to Understand and Construct Proofs", Annie and John Selden, New Mexico State University, Tech. Report No. 2007-1, August 2007, downloadable file, 148KB

2006

• "On the Parallel Lines for Nondegenerate Conics", Rafal Ablamowicz, Department of Mathematics Tennessee Tech and Jane Liu, Department of Civil and Environmental Engineering Tennessee Tech, Tech. Report No. 2006-1, January 2006, downloadable file, 714KB

2004

• "Consciousness in Mathematical Problem Solving: The Focus, the Fringe, and Non-Sensory Perception", John Selden, Department of Mathematical Sciences at New Mexico State Univ. and Annie Selden, Department of Mathematics Tennessee Tech & Department of Mathematical Sciences New Mexico State University, Tech. Report No. 2004-1, April 2004, downloadable file, 163KB
• "A Partial Characterization of the Cocircuits of a Splitting Matroid", Allan Mills, Department of Mathematics Tennessee Tech, Tech. Report No. 2004-2, May 2004, downloadable file, 112KB
• "The Affinity of a Permutation of a Finite Vector Space", W. Edwin Clark, Department of Mathematics University of South Florida, Xiang-Dong Hou, Department of Mathematics University of South Florida, and Alec Mihailovs, Department of Mathematics Tennessee Tech, Tech. Report No. 2004-3, July 2004, downloadable file, 283KB
• "More Than a Seat: Numbers and Symbols in the Cameroon Grasslands", Andrzej Gutek, Department of Mathematics Tennessee Tech, Tech. Report No. 2004-4, July 2004, downloadable file, 198KB
• "Writing DLL in Assembler for External Calling in Maple", Alec Mihailovs, Department of Mathematics Tennessee Tech, Tech. Report No. 2004-5, July 2004, downloadable file, 67KB
• "A Short Note on Strassen's theorem", Motoya Machida, Department of Mathematics Tennessee Tech, Tech. Report No. 2004-6, October 2004, downloadable file, 168KB

2003

• "A Graduate Student's Guide to LATEX and AMS-LATEX", Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, Tech. Report No. 2003-1, February 2003, downloadable file, 387KB
• "Decadal Decline (1992-2002) of Loggerhead Shrikes on Christmas Bird Counts in Alabama, Mississippi, and Tennessee", Stephen J. Stedman, Department of English at Tennessee Tech, and Michael Allen, Department of Mathematics at Tennessee Tech, Tech. Report No. 2003-2, August 2003, downloadable file, 736KB
• "Errors and Misconceptions in College Level Theorem Proving", Annie Selden and John Selden, Department of Mathematics at Tennessee Tech, Tech Report No. 2003-3, August 2003, downloadable file, 92KB
• "A Generalization of a Graph Result of Halin and Jung", Galen E. Turner, III, Mathematics and Statistics, Louisiana Tech University, and Allan D. Mills, Department of Mathematics at Tennessee Tech, Tech. Report No. 2003-4, September 2003, downloadable file, 59KB
• "Set-Valued Duality for Finite-State Markov Chains", James Allen Fill, Department of Mathematical Sciences, Johns Hopkins University, and Motoya Machida, Department of Mathematics at Tennessee Tech, Tech. Report No. 2003-5, October 2003, downloadable file, 288KB
• "Idempotents of Clifford Algebras", Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, B. Fauser, Fachbereich Physik, Universitat Konstanz, K. Podlaski and J. Rembielinski, Department of Theoretical Physics, University of Lodz, Tech. Report No. 2003-6, October 2003, downloadable file, 147KB

2002

• "Tables of Integrals, the Cosecant Function, and Consistency", Brian O'Connor, Department of Mathematics at Tennessee Tech, Tech. Report No. 2002-1, March 2002, downloadable file, 526KB
• "Two Research Traditions Separated by a Common Subject: Mathematics and Mathematics Education", Annie Selden, Department of Mathematics at Tennessee Tech, Tech. Report No. 2002-2, August 2002, downloadable file, 107KB
• "Mathematics of CLIFFORD - a Maple package for Clifford and Grassmann algebras", Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, and Bertfried Fauser, Universitat Konstanz, Germany, Tech. Report No. 2002-4, December 2002, downloadable file, 282KB Revised August 2004, downloadable file, 282KB
• "Clifford and Grassmann Hopf Algebras via the Bigebra Package for Maple(R)", Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, and Bertfried Fauser, Universitat Konstanz, Germany, Tech. Report No. 2002-5, December 2002, downloadable file, 261KB  Revised August 2004, downloadable file, 261KB

2001

• "The Dense Packing of 13 Congruent Circles in a Circle", Ferenc Fodor, Department of Mathematics at Tennessee Tech, Tech. Report No. 2001-1, March 2001, downloadable file, 189KB
• "Clifford Algebra Space Singularities of Inline Planar Platforms", Michael Baswell and Joe N. Anderson, Department of Electrical and Computer Engineering, and Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, Tech. Report No. 2001-2, April 2001, downloadable file,178KB
• "Comparison of Centrality Estimators for Several Distributions", Jamie McCreary, Under the supervision of Dr. Michael Allen, Department of Mathematics at Tennessee Tech, Tech. Report No. 2001-3, April 2001, downloadable file, 619KB
• "Various Estimations of Pi as Demonstrations of the Monte Carlo Method", Jamie McCreary, Under the supervision of Dr. Michael Allen, Department of Mathematics at Tennessee Tech, Tech Report No. 2001-4, July 2001, downloadable file, 73KB

2000

• "Optimal Cylindrical-Block Designs for Correlated Observations", Nizam Uddin, Department of Mathematics at Tennessee Tech, Tech. Report No. 2000-1, March 2000, downloadable file, 189KB
• "On Optimal Row-Column Designs for Two Treatments", David Caughran and Nizam Uddin, Department of Mathematics at Tennessee Tech, Tech. Report No. 2000-2, March 2000, downloadable file, 99KB
• "On the Invertibility of Some Operators on Hilbert Spaces", Ramesh Garimella, Volodymyr Hrynkiv, and Yung-Way Liu, Department of Mathematics at Tennessee Tech, Tech. Report No. 2000-3, June 2000, downloadable file, 166KB

1999

• "The Role of Logic in the Validation of Mathematical Proofs", Annie Selden and John Selden, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-1, February 1999, downloadable file, 171KB
• "On the Separating Ideals of Some Vector-Valued Group Algebras", Ramesh Garimella, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-2, February 1999, downloadable file, 132KB
• "On the Cardinalities of Row Spaces of Boolean Matrices", Michael Breen and David Hume, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-3, April 1999, downloadable file, 45KB
• "Improving Bipartite Graphs Using Multi-Strategy Simulated Annealing", Michael Breen and Panagiotis K. Linos, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-4, April 1999, downloadable file, 59KB
• "Do Calculus Students Eventually Learn to Solve Non-Routine Problems?", Annie Selden, John Selden, Shandy Hauk, and Alice Mason, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-5, May 1999, downloadable file, 95KB
• "Tertiary Mathematics Education Research and its Future", Annie Selden and John Selden, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-6, August 1999, downloadable file, 126KB
• "Hecke Algebra Representations in Ideals Generated by q-Young Clifford Idempotents", Rafal Ablamowicz and Bertfried Fauser, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-7, August 1999, downloadable file, 286KB
• "Perfect Binary Matroids", Allan Mills, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-8, August 1999, downloadable file, 141KB
• "Hecke Algebras, SVD, and Other Computational Examples with Clifford", Rafal Ablamowicz, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-9, September 1999, downloadable file, 499KB
• "On the Decomposition of Clifford Algebras of Arbitrary Bilinear form", Rafal Ablamowicz and Bertfried Fauser, Department of Mathematics at Tennessee Tech, Tech. Report No. 1999-10, November 1999, downloadable file, 334KB