Titu Andreescu

Associate Professor - Science/Math Education
txa051000@utdallas.edu
972-883-2437
FN3308

Professional Preparation

Ph.D. - Mathematics
University of West Timisoara, Romania - 2003
M.S. - Mathematics
University of West Timisoara, Romania - 1980
B.A. - Mathematics
University of West Timisoara, Romania - 1980

Research Areas

Research Interests

1. Enhancing students interests and skills in mathematics.
I am the Director and Founder of AwesomeMath, which includes a summer program for students training to succeed at the Olympiad level, a correspondence-based lecture series for students continuing education, called AwesomeMath Year-round, and Mathematical Reflections, a free online journal focused primarily on mathematical problem solving. The main purpose of this initiative is to give students an opportunity to engage in meaningful learning activities and explore in detail areas in advanced mathematics. AwesomeMath's primary focus is on problem-solving. I use it as a tool to enhance students' interest and skills in mathematics.

I believe that there are two major parts in significant mathematics teaching and learning: higher concepts (introducing and developing new topics) and applying those concepts creatively to concrete problems (bringing life to the new topics). These two areas rely on each other, but we focus primarily on the latter. I feel that certain advanced mathematics topics are best introduced to young students by motivating the concepts through problems that encourage investigation. 

I am actively involved with mathematics competitions at the secondary and undergraduate levels.  I write and contribute questions for the American Mathematics Competitions examinations as well as the International Mathematics Olympiad and the W. L. Putnam competition. 

I would like to involve undergraduate students in my research.  My area of research is an ideal entrance point to research for talented students, since it does not require a lot of background while offering abundance of open problems.  In addition to the problems I can suggest, the students can also easily make their own conjectures, experiment by using Computer Algebra Systems, attack special cases, generalize and transfer ideas from one case to another, and learn and use various techniques while trying to resolve the problems.  Thus they would experience first hand all the phases and subtleties of doing original research.

2. Diophantine Analysis, with emphasis on Quadratic Diophantine Equations.
 This research area focuses especially on the study of the general Pell's equation, which is connected to problems from various domains of mathematics and science, such as Thue's Theorem, Hilbert's Tenth Problem, Euler's Concordant Forms, Einstein's Homogeneous Manifolds, Hecke Groups, and so forth.  I have obtained numerous original results such as:  

  1. In the cases when the equation is solvable, I found an elegant explicit form for the solutions.  I then extended a result of D. T. Walker [The American Mathematical Monthly, vol. 74, no. 5, 1966, 504-513].
  2. I proved partial results about the equation  and formulated conjectures regarding its solvability.
  3. I obtained results about the equation , including those regarding the LMM algorithm of finding the fundamental solutions to the general Pell's equation based on continued fractions.
  4. I devised two original methods of solving the equation .
  5. I proved that numerous important quadratic equations have infinitely many solutions in integers.

I devoted special attention to the Diophantine representability of several interesting sequences of positive integers.  I introduced the concept of r-Diophantine representability of a sequence of positive integers and studied in an original manner the equations  by employing the special Pell's equation .  I have extensively studied the Diophantine representability of the Fibonacci, Lucas, and Pell sequences using methods of investigation different from and simpler than the ones already found in the literature.  I also studied the problem of Diophantine representability of generalized Lucas sequences, which I introduced, finding conditions under which their general solution is a linear combination with rational coefficients of the classical Fibonacci and Lucas sequences. 

I found numerous applications of the results above.  For example, I determined conditions under which the numbers  and  are simultaneously perfect squares for infinitely many positive integers n.  I discovered special properties of triangular numbers, such as proving that any positive rational number r, where is irrational, can be written as the ratio of two triangular numbers.  I extended some results pertaining to triangular numbers to polygonal numbers.

Publications

T. Andreescu, W. Stromquist, Z. Sunik, Bandwith Reduction in Rectangular Grids. Discrete Mathematics, accepted ? - Publication
T. Andreescu, D. Andrica, Diophantine Representations of Some Generalized Lucas Sequences, The Fibonacci Quarterly, submitted ? - Publication
T. Andreescu, D. Andrica, On the Diophantine Equations XZ + my + WZ Z i 1, The Fibonacci Quarterly, submitted ? - Publication
T. Andreescu, On a Class of Diophantine Equations, American Mathematical Monthly, submitted ? - Publication
T. Andreescu, D. Andrica, Complex Numbers from A to Z Birlchauser Boston, 2005, 364 pp. 2005 - Publication
T. Andreescu, D. Andrica, An Introduction to Diophantine Equations, GIL Publishing House, 2002, 198 pp. Also published in Romanian as: O introducere in studiul ecuatiilor diofantiene, Editura GIL, 2002, 202 pp. 2005 - Publication
T. Andreescu, O. Muskarov, L. Stoyanov, Minima and Maxima in Geometry, Birkhauser Boston, 2005, 264 pp. 2005 - Publication
T. Andreescu, D. Andrica, On a Diophantine Equation and its Ramyications, The College Mathematics Journal, 1(2004) (MR 2023403) 2004 - Publication
T. Andreescu, Z. Feng, P.-S. Loh, editors, USA and International Mathematical Olympiads 2004, Mathematical Association of America, Mathematical Association of America, to appear. 2004 - Publication
T. Andreescu, Z. Feng, editors, USA and International Mathematical Olympiads 2003, Mathematical Association of America, 2004, 86 pp. 2004 - Publication

Appointments

Associate Professor
University of Texas at Dallas (UTD), Richardson TX [2005–Present]
Science/Mathematics Education Department
Visiting Scholar
Tokai University, Tokyo, Japan [2003–2003]
Visiting Scholar
University of Wisconsin-Whitewater (UWW), Whitewater, Wl [2003–2004]
Director
University of Nebraska-Lincoln (UNL), Lincoln, NE [1998–2003]
Mathematics Teacher
Illinois Mathematics and Science Academy (IMSA), Aurora, IL [1991–1998]
Mathematics Teacher
Loga Academy, Timisoara, Romania [1980–1990]

Projects

Consultant to the Iberoamerican Mathematics Olympiad in Puerto Plata, Dominican Republic
1999–1999
Opening lecturer at Canada/USA
2000–2000 Opening lecturer at Canada/USA Math Camp in Toronto, Canada, July, 2000
Seminario de Educacion Matematica lberoamericano con `Enfasis en solucion de Problemas
2005–2005 Seminario de Educacion Matematica lberoamericano con `Enfasis en solucion de Problemas, Cartagena, Colombia
Delivered a series of lectures to students and secondary teachers in Taipei and other major cities throughout Taiwan
2002–2002
Mathematical Induction, an Elegant and Powerful Method
1998–1998 University of South Wales in Sidney, Australia

Additional Information

Other Student Activities

1995-2002 Director of the Mathematical Olympiad Summer Program (MOSP) and Leader of the US delegation to the IMO. In addition to MOSP teaching responsibilities, oversaw the work of the other instructors and closely supervised their teaching.

1994-2002 Head Coach of the USA Mathematical Olympiad Team. Led the US team to its historic lst place in 1994 when all six American students achieved perfect scores, unique performance in the 45-year history of the IMO. Led Team USA to 2"d place in 1996 and 2001, and 3rd place in 1998, 2000, and 2002 in a field of more than 80 participating countries.

1993-1999 Grading room chair of American Regions Mathematics League (ARML)

1993-1994 and 2003—Present Assistant Coach of the USA IMO Team


1991-1998 Coach of the Chicago Area All-star Mathematics Team

1991 -1998 Co-sponsor of the IMSA chapter of Mu Alpha Theta

1983-1989 Counselor, Romanian Ministry of Education. Designed and implemented specialized programs to optimize the education of gifted middle and high school students, involving close interaction with university professors and senior teachers associated with Romania's best secondary schools. Assistant Coach of the Romanian Mathematics Olympiad Team and Deputy Leader of the Romanian Team for the Mathematical Contest of the Balkan Countries and the IMO.

References
Dr. Tom Butts
School of Natural Sciences and Mathematics
University of Texas at Dallas
Richardson, TX 75080
tbutts@utdallas.edu

Dr. Jonathan Kane
Department of Mathematical and Computer Sciences
University of Wisconsin - Whitewater
Whitewater, W1 53190-1790
262-472-5002
kanej@uww.edu

Dr. Ken Ono
Solle P. and Margaret Manasse Professor of Letters and Science
Department of Mathematics
University of Wisconsin
Madison, Wisconsin 53706
608-263-2604
ono@math.wisc.edu

Dr. Zoran Sunik
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
979-862-2182
sunik@math.tamu.edu

Dr. Dorin Andrica
Faculty of Mathematics and Computer Science
Babes-Bolyai University
Str. Kogalniceanu l
Cluj-Napoca, Romania
0l l-402-64-215956
dorinandrica@yahoo.com

Dr. Steven Condie
Illinois Mathematics and Science Academy
l500 W. Sullivan Road
Aurora, IL 60506
630-907-5967
scondie@imsa.edu

Dr. Razvan Gelca
Texas Tech University
Lubbock, TX 79409
806-742-2584
rgelca@math.ttu.edu

Other Student Activities
  • Hotchkiss School, Lakeville, CT, 2005
  • MAA Sectional Meeting, Arlington, TX, 2005
  • Mathematical Sciences Research Institute, Berkeley, CA, 2004
  • University of Puget Sound, WA, 2003
  • University of Colorado, Colorado Springs, CO, 2002
  • MathPath, Black Hills State University, Spearfish, SD, 2002
  • University of California at Los Angeles, CA, 2002
  • Texas Tech University, TX, 2002
  • MAA Sectional Meeting, Ripon, WI, 2002
  • Ohio University, Athens, OH, 2002
  • Phillips Exeter Academy, NH, 2002
  • Hunter College, NY, 2002
  • Stuyvesant High School, NY, 2002
  • University of South Alabama, AL, 2001
  • Colby College, ME, 2001
  • Brooklyn Tech High School, NY, 2001
  • Academy for Advancement of Science and Technology, NJ, 2001

Funding

MAA American Mathematics Competitions
$600,000 - Akamai Technologies [2000–2002]
MAA American Mathematics Competitions
$50,000 - U.S. Army Research Office [2000–2001]
MAA American Mathematics Competitions
$162,835 - U.S. Office of Naval Research [1999–2002]