Me 
My subject 
Doug Hensley, Professor
- BLOC 206C
- email: dhensley@math.tamu.edu
- Math Circle
Math Circle discussion of Long Division, the GCD, and more with pictures and and a post-script with more pictures.. How to find GCDs and modular inverses. How to run numbers up to big powers fast in modular arithmetic. What it's good for.
-
- Denton Dynamics-relevant material. Acta Arithmetica 153.1, 2012 joint paper.
TAMU Freshman-Sophomore Contest (Yearly, in the Spring)
- Solutions to 2018 contest, first year solutions , and second year solutions. The first three problems were common to both versions.
Winners will be announced shortly.
- Solutions to 2017 contest, first year solutions , and second year solutions.
- Solutions to 2014 contest, first year solutions , and second year solutions.
- Solutions to 2013 contest, first year solutions, and second year solutions.
- Solutions to 2012 contest, first year solutions, and second year solutions.
- Solutions to 2011 contest, Amalgamated solutions to both versions.
- Solutions to 2010 contest, First year , and second year.
- Solutions to 2009 contest, First-year , and second year.
Continued Fractions-Book Supplements and Errata
- Page 113, line -6, $|\sum_1^n s_j{\bf b}_j|\ge |{\bf b}_d|$ (reverse direction of inequality)
- Page 141, line 4, on the RHS, multiply by $\rho({\bf c})$.
- Page 228, exp[z]=1+2z/(2-z+z^2/(6+z^2/(10+z^2/(14+...)))). (There is no (2+z^2 before the 6+z^2).
- Page 171, LHS of first display should read G-G_N, not G-G_n.
- The Hermite continued fraction Hermite algorithm Mathematica notebook .
- The Lagarias geodesic multidimensional continued fraction Mathematica notebook algorithm implemented in Mathematica.
A version compatible with Mathematica 6.* .
- Another proof of the theorem of Stern and Stolz; conceptually quite simple, computationally a bit of a pain absent computer algebra.
- Jerry Lange's converse Mathematica notebook to the theorem of Stern and Stolz.
- Mathematica notebook concerning the Zaremba conjecture to the effect that for all n there exists k such that the continued fraction expansion of k/n involves only partial quotients no greater than 5. Also treats the possibility that for sufficiently large n, 5 can be replaced by 2.
- Note that Bourgain and Kontorovich have recently obtained a strong result in the direction of the Zaremba conjecture: there exists an (explicit, reasonably small e.g. 3000) positive integer q such that for almost all n, there exists k such that the continued fraction expansion of k/n involves only partial quotients less than q.
- The analogue of the Gauss density for the Hurwitz complex continued fraction algorithm.
- Notebook documenting computations related to the growth rate of Abs[q_n] in the Hurwitz complex continued fraction algorithm.
Buzz Contest
- Short version of the rules, updated Oct 20 2017. Buzz contest words and rules., Together with tricks of the trade and reasons behind them. Updated Oct 20 2017 for the upcoming buzz contest.
- Buzz contest take on the reasons behind the connection between solutions to u=a*a+b*b and the prime factorization of u. PDF file here.
High School Circle
- High School Circle 2010 Calculus problem, high school solution , underlying mathematica notebook for cphss,
archimedes gets the area inside a chord and a parabola, underlying mathematica notebook for archygeom.
- Final exam solutions Math 152, 2007 Solutions to the final exam for Math 152, Friday May 4, 2007. including questions, solutions, and further remarks.
Freshman-Sophomore Contest 2008
- This was held Monday April April 21. Here are solutions: Freshman Version solutions , and Sophomore version solutions. Some of the problems were common to both versions.
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Winners were Siying Peng, Kenneth Taliaferro, William Sames, Louis Tronzo, and Luiz Faria, respectively first, second, third, and tied for 4th-5th.
- Freshman-Sophomore Contest 2007: This was held Monday April 30.
Here are solutions to both the first-year and second-year
versions: Freshman Version Solutions,
Sophomore Version Solutions.
The first three problems were common to both versions. Winners were:
First place, Gleb Zhelezov.
Second place, Zack Darwin and Karthic Gopavaram (tie).
Fourth place, Joseph Stratton.
Fifth place, Shyam S. Kumar.
Sixth place, Luiz Faria and Kenneth Taliaferro (tie).
Math 152H Fall 2006
- First day handout math 152H, Fall 2006. as Adobe PDF file.
- Math 152H home page .
- Math 490 first day handout.
- Math 304 first day handout.
ArithmeTexas Items
- Number Theory Seminar Sept 21 notes link here .
- Link to Complex Continued Fractions , in particular, the Hurwitz complex continued fraction.
- Link to buzzrules .
- Office hours Spring 2006 Monday 1-3, Wed. 3-4 or by appointment. You can use email [Doug.Hensley@math.tamu.edu] to arrange other times.
Math 411 Spring 2006
- First day handout math 411, Spring 2006. as Adobe PDF file.
Math 427 Fall 2005
- First day handout link as Adobe PDF file.
- Leveque page 1 Chebyshev proof link 1
- page 2 link 2
- page 3 link 3
Math 411 Spring 2005
- First day handout math 411, Spring 2005. as Adobe PDF file.
- Home page for math 411, Spring 2005.
Math 302 Fall 2003
- Math 302 Fall 2003 instructor's homepage. link .
- Home page for math 302, Spring 2002 click here link.
Freshman-Sophomore Contest 2006.
- Problems and solutions, first year version and second-year version.
- winners of the 2006 TAMU math department's Freshman-Sophomore Contest.
Freshman-Sophomore Contest 2004.
- Problems for both brackets , and first year, and second year contestants.
.
Putnam Challenge Math 490. The Deep Pool. Dive right in.
- First class for Fall 2004 will be held Wed Sept 1, 7 PM, Milner 317. Somebody will be at the front door of Milner to let you in, because normally the doors are locked after 5PM.
- Home page for math 302, Spring 2004.
(That was a typo. It's Fall).
Freshman-Sophomore Contest April 8, 2003
- The winners in the Freshman-Sophomore Contest are:
(1) Brian Hyams
(2) Steven Houston
(3) Kyle Marshall
(4) Gregory Prill
(5) Chad Wellington
(6) Chris O'Brien
Prizes were $150, 125, 100, 80, 60, 50.
Congratulations to all winners, and for the `losers', this observation: there is no disgrace in being edged out by competitors of this caliber.
- The curve has the formula e to the power (-C*(x squared)) times cos(Kx). For more details, see this dotps link.
- Solutions page 1 and freshman page 2 and sophomore p. 2 .
Freshman-sophomore contest 2001
- Freshman-Sophomore contest solutions. Stay tuned to this space for contest results when they become available. Post-script solutions with new graphics added: some solutions . the rest of the solutions And in pdf format, some solutions and the rest of the solutions .
Winners have been announced in class. The winners were: winners list, Adobe pdf file
Freshman-sophomore contest 2002
- Winners list pdf file.
- Freshman-sophomore contest solutions. Freshman solutions pdf file here . This file includes solutions to the three problems from page 1 of the sophomore contest, because those three problems were common to both contest problem sets. Stay tuned for solutions to the other three sophomore problems.
And here they are: sophomore solutions .
Teaching
- Math 304 supplementary material. link. .
- Previous semester Math 601 supplementary material. link .
- psfig is freeware with the usual restrictions about not copying it and then selling it. link here
- Syllabus and first day handout for math 251, Fall 2001 Adobe pdf version or raw text TeXfile .
- Instructor's home page for math 251, Fall 2001 enter here .
- Syllabus and first day handout for math 302, Spring 2001 Adobe pdf version or ASCII text version .
- Solutions to exam 1 Spring 2001 math 302 link here . This link will go operational sometime Tuesday evening.
- Solutions to exam 2 Spring 2001 math 302 link here
- Solutions to exam 3 click here for exam 3 solutions
- Solutions to one of the finals for Math 302 Spring 2001: pdf format as usual.
- Syllabus and first day handout for math 302, Fall 2000 click here for Adobe pdf version or here for ASCII .
- Solutions to exam 1 adobe pdf format . Magnify this for better viewing and printing...pdf gives sometimes strange results when the pixels are too nearly equal in size to the characters. Same for solutions to the second exam .
- Solutions to final exam Fall 2000 math 302 pdf file .
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- Syllabus and first day handout for math 151, Spring 2000 link here
- Instructor's home page for Math 151, Spring 2000 link . Bookmark this link.
- Instructor's home page for Math 312, Spring 2000 link . Bookmark this link.
- Syllabus and first day handout for math 312, Spring 2000 link here
- First Maple sheet here.
- Another two Maple sheets , to look at .
- Syllabus and first day handout for Math 311, Fall 1999 adobe pdf format .
- Text is available at Copy Corner, 1404 Tx Ave S., tel 694-copy.
- Home page for Fall 1999 Math 311.
- Discrete mathematics Math 302 home page.
- Solutions to exam 3 here .
- Electronic handout for Math 302-Spring 99 on FFT . Associated Mathematica notebook.
- Final exams from past years in Math 302: 98 , 97 , and 96 .
- Math 152, Engineering Calculus II. Syllabus and first day handout here. Remarks on the fundamental theorem of calculus.
- Math 152 Individual Instructor Home Page
. Look here for Maple sheets and etended discussion of the lectures.
- Math 629, History of Mathematics (coming this Spring to a classroom near you.) What's in store? Click on the link.
- Differential Equations Math 308 Section 510 syllabus and first day handout. Post-script version .
- Home page for math 308 section 510.
- Math 311 tex file for syllabus. post-script (more readable) version.
- Math 311 solutions to exam 1
- Math 311 Maple handout. (Executable version).
- Math 311 Viewable via Netscape version of handout.
- Math 311 Now it IS posted answersheet.
- Math 311 solutions to exam 2.
- Math 311 solutions to exam 3. PDF format solutions.
- Math 308_506 HOME PAGE
- Math 311 Mma notebook viewer
- Math 311 solutions postscript file.
- Math 311 pdf version.
- Number Theory 627, Summer Session II. syllabus .
- shadows .
- Maple for 627, Intro Sheet .
- Work for lab week 3, Maple file .
- Mobius Maple sheet.
- Combinatorics and discrete math , math 302.
- Differential equations math 308-504 syllabus. For some material from past semesters, click here.
- Spring 1997 differential equations home page.
- Other courses.
Texas A&M Freshman-Sophomore Math Contest results.
- For contest purposes, freshman means anyone who is in their first year of post-highschool studies, and sophomore, anyone in their second year. Those 9 hours of AP History you got don't push you over into Junior status, in other words.
- Problems and solutions Y2K. Freshman and sophomore contestants had the same problems in common for the first page, but the second page problems were different. this link gives the solutions to the common problems and to the second page's freshman problems. Sophomore problem solutions to questions 4, 5, and 6 will be posted shortly. (And here they are.
- Links below show some problems and solutions from past years.
- 1999 Freshman problems and solutions. (SOPH AVAILABLE FRIDAY) like now
- The 1999 winners circle.
- 1998 PROBLEMS AND SOLUTIONS .pdf Adobe Portable Document Format readable files first 3 questions , freshmen-only questions , and sophomore-only questions . Typo in p1 solutions, last number is -3 not -2.
- 1998 Winners and honorable mentions: click here .
- The 1997 contest. Tex file. .
- The winners circle.. See if you won.
- The TeX file for solutions.
- PDF solutions file . Maple file related to all this. Maple cube2c.mws file , ready for execution. Pretty pictures of the portion of a cube nearer the center than any of the corners.
- Maple file for the systems problem.
- List of 1996 winners. Sample page from the 1995 contest. Post-script files of the 1996 questions: page 1, Freshman contest page 2, and sophomore contest page 2.
- Maple sheet which plots that function on the Freshman-sophomore contest.
Research
Research Interests
- Number Theory
- Continued fractions
- Convexity
- Selected Publications and the full list available, some with related graphics.
- Mathematica 3.0 notebook related to C-Fraction expansions.
- Mathematica notebook implementing the Lagarias geodesic multidimensional continued fraction expansion for rational inputs.
- Badly approximable vectors and their multiples mod 1 . Illinois AMS conference March 1999.
- Mathematica notebook illustrating one of the results of the above paper.
- Mathematica dotm file related to the Hurwitz complex continued fraction.
- The number of steps in the Euclidean algorithm
Education
- B.S. University of Kansas 1970
- Ph.D. University of Minnesota 1974.