William Yslas Velez
 Advisor, Recruitment
Contact
 (520) 6216892
 MATHEMATICS, Rm. 108
 velez@email.arizona.edu
Degrees
 Ph.D. Mathematics
 University of Arizona, Tucson, Arizona, United States
 A basis for the group of units modulo Pm and prime ideal factorization in F(a1/m).
Awards
 The William Yslas Vélez Outstanding Science, Technology, Engineering and Mathematics in Higher Education Award
 Award created by The Victoria Foundation, Fall 2015
 Gweneth Humphreys Award for Mentorship of Undergraduate Women in Mathematics
 Association for Women in Mathematics, Spring 2014
Interests
No activities entered.
Courses
201617 Courses

Intro to Linear Algebra
MATH 313 (Spring 2017) 
Intro to Linear Algebra
MATH 313 (Fall 2016)
Scholarly Contributions
Journals/Publications
 Rose, C., & Barr, T. (2016). 2015–2016 Faculty Salaries Report. Notices of the American Mathematical Society, Volume 63(Number 4), 390396.
 Rose, C., & Barr, T. (2016). Fall 2014 Departmental Profile Report. Notices of the American Mathematical Society, Volume 63(Number 2), pp. 163173.
 Rose, C., & Barr, T. (2016). Report on 2014–2015 Academic Recruitment, Hiring, and Attrition. Notices of the American Mathematical Society, Volume 63(Number 4), 383387.
 Rose, C., & Barr, T. (2016). Report on the 2014–2015 New Doctoral Recipients. Notices of the American Mathematical Society, Volume 63(Number 7), 754765.
 Thomas, M., & Barr, T. (2016). Recent Trends in Bachelors Degree Recipients in Mathematics at US Institutions. Notices of the American Mathematical Society, Volume 63(Number 6), 660665.
 Velez, W. Y. (2014). 20132014 Faculty Salaries Report. Notices of the AMS, 61(6), 611617.More infoCoauthors: William Yslas Vélez, James W. Maxwell, and Colleen RoseAs chair of the data committee I take an active role in the preparation of these reports. The data is from the annaul surveys and staff from the AMS prepare the reports. I have input as to the content and I proofread every document.
 Velez, W. Y. (2014). Mathematics Instruction, An Enthusiastic Activity, William Yslas Vélez,. AMS Blogs, On Teaching and Learning Mathematics, 1.
 Velez, W. Y. (2014). Preliminary Report on the 2012–2013 New Doctoral Recipients,. Notices of the AMS, 61(6), 618620.More infoCoauthors: William Yslas Vélez, James W. Maxwell, and Colleen Rose
 Velez, W. Y. (2014). Report on 20122013 Academic Recruitment and Hiring, ,. Notices of the AMS, 61(7), 744749.More infoCoauthors: William Yslas Vélez, James W. Maxwell and Colleen Rose
 Velez, W. Y. (2014). Report on the 20122013 New Doctoral Recipients,, , Volume 61, Number 8, September 2014, pp 874884.. Notices of the AMS, 61(8), 874884.More infoCoauthors: William Yslas Vélez, James W. Maxwell, and Colleen Rose
 Velez, W. Y. (1999). Minority data [9]. Science, 285(5432), 13571358.
 Mora, F. B., & Velez, W. Y. (1993). Some Results on Radical Extensions. Journal of Algebra, 162(2), 295301.
 Lee, J. ., & Vélez, W. (1992). Integral solutions in arithmetic progression for y^{2}=x^{3}+k. Periodica Mathematica Hungarica, 25(1), 3149.More infoAbstract: Integral solutions to y 2=x 3+k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y's formed an arithmetic progression of length 4 had already been constructed. In this paper, we construct infinitely many sets of solutions where there are 4 x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where there are 4, 5 and 6 y's in arithmetic progression. © 1992 Akadémiai Kiadó.
 Jacobson, E. T., & Vélez, W. Y. (1990). The Galois group of a radical extension of the rationals. Manuscripta Mathematica, 67(1), 271284.More infoAbstract: The Galois group of the splitting field of an irreducible binomial x 2 e a over Q is computed explicitly as a full subgroup of the holomorph of the cyclic group of order 2 e . The general case x n a is also effectively computed. © 1990 SpringerVerlag.
 Jacobson, E., & Vélez, W. Y. (1990). Fields arithmetically equivalent to a radical extension of the rationals. Journal of Number Theory, 35(3), 227246.
 Vélez, W. Y. (1988). On a property of cosets in a finite group. Journal of Algebra, 115(2), 412413.
 Jacobson, E., & Vélez, W. Y. (1985). On the Adèle rings of radical extensions of the rationals. Archiv der Mathematik, 45(1), 1220.
 Vélez, W. Y. (1985). Several results on radical extensions. Archiv der Mathematik, 45(4), 342349.
 Acosta, M., & Velez, W. Y. (1984). The torsion group of a field defined by radicals. Journal of Number Theory, 19(2), 283294.More infoAbstract: Let L F be a finite separable extension, L* = L{0}, and T( L* F*) the torsion subgroup of L* F*. When L F is an abelian extension T( L* F*) is explicitly determined. This information is used to study the structure of T( L* F*). In particular, T( F(α)* F*) when am = a ∈ F is explicitly determined. © 1984.
 Orozco, M. d., & Vélez, W. Y. (1982). The lattice of subfields of a radical extension. Journal of Number Theory, 15(3), 388405.More infoAbstract: Let xm  a be irreducible over F with char F{does not divide}m and let α be a root of xm  a. The purpose of this paper is to study the lattice of subfields of F(α) F and to this end C( F(α) F, k) is defined to be the number of subfields of F(α) of degree k over F. C( F(α) F, pn) is explicitly determined for p a prime and the following structure theorem for the lattice of subfields is proved. Let N be the maximal normal subfield of F(α) over F and set n = N : F, then C( F(α) F, k) = C( F(α) F, (k, n)) = C( N F, (k, n)). The irreducible binomials xs  b, xs  c are said to be equivalent if there exist roots βs = b, γs = a such that F(β) = F(γ). All the mutually inequivalent binomials which have roots in F(α) are determined. Finally these results are applied to the study of normal binomials and those irreducible binomials x2e  a which are normal over F (char F ≠ 2) together with their Galois groups are characterized. © 1982.
 Mann, H. B., & Vélez, W. Y. (1976). Prime ideal decomposition in {Mathematical expression}. Monatshefte für Mathematik, 81(2), 131139.More infoAbstract: Let F be an algebraic number field and μ∈F such that xmμ is irreducible, where m is an integer. Let {Mathematical expression} be a prime ideal in F with {Mathematical expression}. The prime decomposition of {Mathematical expression} in {Mathematical expression} is explicitly obtained in the following cases. Case 1: {Mathematical expression}, (a,m) = 1 (where {Mathematical expression} means {Mathematical expression}, ς ≢ 0 {Mathematical expression}). Case 2:m ≡lt, where l is a prime and l ≢ 0 {Mathematical expression}. Case 3:m ≢ 0 {Mathematical expression} and every prime that divides m also divides pf1. It is not assumed that the vth roots of unity are in F for any v ≠ 2. © 1976 SpringerVerlag.