## Nov 26, 2015

### Pigeonhole Principles and its application

http://www.artofproblemsolving.com/wiki/index.php/Pigeonhole_Principle

1. Seven line segments, with lengths no greater than 10 inches, and no shorter than 1 inch, are given. Show that one can choose three of them to represent the sides of a triangle. (Solution)
2. Prove that having 100 whole numbers, one can choose 15 of them so that the difference of any two is divisible by 7. (Solution)
3. Prove that from any set of one hundred whole numbers, one can choose either one number which is divisible by 100, or several numbers whose sum is divisible by 100. (Solution)
4. Prove that among any ten points located on a circle with diameter 5, there exist at least two at a distance less than 2 from each other. (Solution)
(Japan 1997)
5. Every point in a plane is either red, green, or blue. Prove that there exists a rectangle in the plane such that all of its vertices are the same color. (Solution)
(USAMTS Year 18 - Round 1 - Problem 4)
6. There are 51 senators in a senate. The senate needs to be divided into committees such that each senator is on exactly one committee. Each senator hates exactly three other senators. (If senator A hates senator B, then senator B does 'not' necessarily hate senator A.) Find the smallest such that it is always possible to arrange the committees so that no senator hates another senator on his or her committee. (Solution)

### Generating functions for series

and 2nd edition here:

## May 7, 2015

### Searching for Mathematical Tripos resources

http://math.stanford.edu/~lekheng/tripos/

` math-tripos-pre1878.pdf  11-May-2010 15:02   16M`
` math-tripos1908-1912.pdf 11-May-2010 14:59  1.1M `
` math-tripos1913-1917.pdf 18-Aug-2014 23:00  4.7M  `
```
```
`http://math.cmu.edu/~cnewstea/notes/source/RTexsheet1.pdf`
`http://math.cmu.edu/~cnewstea/notes/source/RTexsheet2.pdf`
```
```
`http://tartarus.org/gareth/maths/stuff/lecturelist2012-13.pdf`
```
```
`http://www.ams.org/journals/bull/1906-13-03/S0002-9904-1906-01433-1/S0002-9904-1906-01433-1.pdf`
```
```
```
```
`https://www0.maths.ox.ac.uk/system/files/coursematerial/2014/3109/32/2006_Noetherian_Algebras_exam.pdf`
`http://www.archim.org.uk/lecturenotes/ia/notes.pdf`

Thirsting for more?

https://goo.gl/rQjSog

And just a sampling of the above:

• ### MATHEMATICAL TRIPOS Part III PAPER 54 ...

MATHEMATICAL TRIPOS. Part III. Tuesday, 3 June ... Attempt no more than THREEquestions. There are FOUR questions in total. The questions carry equal  ...
• ### [PDF]MATHEMATICAL TRIPOS Part III PAPER 7 TOPICS IN ...

MATHEMATICAL TRIPOS. Part III. Monday, 9 June ... Attempt no more than THREEquestions. There are FOUR questions in total. The questions carry equal  ...
• ### MATHEMATICAL TRIPOS Part III PAPER 27 STOCHASTIC ...

MATHEMATICAL TRIPOS. Part III. Thursday, 5 June, 2014 ... Attempt no more than FOUR questions. There are SIX questions in total. The questions carry equal  ...
• ### MATHEMATICAL TRIPOS Part III PAPER 74 ...

MATHEMATICAL TRIPOS. Part III. Monday, 2 June ... Attempt no more than THREEquestions. There are FOUR questions in total. The questions carry equal  ...
• ### [PDF]MATHEMATICAL TRIPOS Part III PAPER 66 NUMERICAL ...

MATHEMATICAL TRIPOS ... Attempt no more than THREE questions from Section A... The questions in Section B carry twice the weight of those in Section A.
• ### [PDF]GUIDE TO ADMISSIONS in MATHEMATICS - Faculty of ...

Mar 20, 2015 - Tripos produced by the Faculty of Mathematics (available on our web ....of success in the Mathematical Tripos, partly because the questions.
• ### [PDF]MATHEMATICAL TRIPOS Part III PAPER 65 CONVEX ...

MATHEMATICAL TRIPOS. Part III. Tuesday, 3 June, 2014 ... Attempt no more than FOUR questions. There are FIVE questions in total. The questions carry equal  ...

• ## Feb 4, 2015

### Bay Area Mathematical Olympiad & Berjekey Math Circle

Lots of problems (BAM Olympiad) from 1999 to 2014:

## Jan 17, 2015

### Mathematical problems and puzzles for your entertainment

From below is an endless source of mathematical puzzles and problems for your weekend:

http://goo.gl/B22QuS

A snapshot highlights of the above is listed below:

1. ### [PDF]Fall semester 2012 September 28, 2012 MATHEMATICS ...

Nov 19, 2012 - Fall semester 2012. September 28, 2012. MATHEMATICS DEPARTMENT CONTEST. The Department of Mathematics invites all CUA students ...
2. ### [PDF]Spring semester 2014 January 31, 2014 MATHEMATICS ...

Jan 31, 2014 - Spring semester 2014. January 31, 2014. MATHEMATICS DEPARTMENT CONTEST. The Department of Mathematics invites all CUA students ...
3. ### [PDF]Fall 2014 Math Contest - Department of Mathematics

Aug 25, 2014 - Fall semester 2014. August 25, 2014. MATHEMATICS DEPARTMENT CONTEST. The Department of Mathematics invites all CUA students to ...
4. ### [PDF]here - Department of Mathematics

Mathematics Department Contest. Spring, 2008. The Department of Mathematics invites all CUA students to compete, for the fun of it, in a mathematics contest.
5. ### [PDF]Spring semester 2012 January 19, 2012 MATHEMATICS ...

Jan 19, 2012 - Spring semester 2012. January 19, 2012. MATHEMATICS DEPARTMENT CONTEST. The Department of Mathematics invites all CUA students ...

http://soltreemrls3.s3-website-us-west-2.amazonaws.com/marzanoresearch.com/media/documents/reproducibles/highly_engaged/mathematics.pdf

https://www.math.ucdavis.edu/~gravner/MAT135A/resources/chpr.pdf

https://math.dartmouth.edu/~pw/solutions.pdf

http://www.math.msu.edu/~ywang/Preprints/three-hat.pdf

1. ### [PDF]Seven Puzzles You Think You Must Not Have Heard Correctly

A typical mathematical puzzle sounds tricky but solvable—if not by you, then ... Note: You won't need to know any mathematics to understand the puzzles, but a ...
2. ### [PDF]Twenty problems in probability - UC Davis Mathematics

This section is a selection of famous probability puzzles, job interview ... tech companies ask their applicants math questions) and math competition problems.
3. ### [PDF]Math is a puzzle

We accepted articles on any math puzzle that was interesting, We received articles written about how to prove different types of mathematical puzzles. In order ...
4. ### [PDF]Mathematical Games and Puzzles By John Dale Hudson

https://math.ucsd.edu/programs/...of_math.../math_history_06.pdf
A Brief Look at Mathematical Games and Puzzles of the 18th and 19th ... Mathematical puzzles, questions, and games have a rich history spanning from the.
5. ### [PDF]THE THREE-HAT PROBLEM 1. Introduction Many classical ...

by B BENSON - ‎Related articles
The Three-Hat Problem is one of such puzzles. ... As far as we know, both puzzles were proposed by Donald Aucamp in the MIT ... mathematical logic.
6. ### [PDF]GAMES, PUZZLES, RECREATIONAL MATH HARM ...

www.math.lsa.umich.edu/~hderksen/math289.../math289/PS7games.pdf
PROBLEM SET 7: GAMES, PUZZLES, RECREATIONAL MATH. HARM DERKSEN. 1. Weighing Problems. There are many popular problems involving weighing ...
7. ### [PDF]Geometry Puzzles

www.math.washington.edu/~mathcircle/mmc/mmc2009/Geometry.pdf
Geometry Puzzles. Problem 1 (But first, one last logic puzzle). Suppose that you are a prisoner, and you are con- fronted with two doors: one leading to freedom, ...
8. ### [PDF]1 A Brief Introduction to the Mathematics of Chess Puzzles 2 ...

Puzzles on the chessboard have long been studied by mathematicians. Nat# ... The closed knight`s tour of a chessboard is a classic problem in mathematics.
9. ### [PDF]Mathemagics: Teaching Math with Games and Puzzles

Mathemagics: Teaching Math with Games and Puzzles. Dr. Lee Eimers. Cedarville University. ACSI Dayton 2003. Questions you might ask? Why would we ...
10. ### [PDF]Math 103 Lecture 1 notes Types of Problems: 1. Process ...

Translation: include one- and two-step story problems typically found in ... Puzzles: solving puzzles may not require any mathematical knowledge, but are.

## Jan 15, 2015

### Study of prime numbers and polyhedra

Scanning through these pictures will give you so much joys and appreciation of beauty of maths:

## Jan 10, 2015

### Mathematics of curves & geometry

Keen to learn about curves and geometry?  Check this out:
A selection of the above links are listed below:
1. ### [PDF]ALGEBRAIC CURVES - Mathematics

www.math.lsa.umich.edu/~wfulton/CurveBook.pdf
by W FULTON - ‎2008 - ‎Cited by 35 - ‎Related articles
Jan 28, 2008 - of the topics covered in this text: linear series on curves, intersection ... gebra background to a few of the ideas of algebraic geometry and to ...
2. ### [PDF]DIFFERENTIAL GEOMETRY: A First Course in Curves and ...

by T Shifrin - ‎2014 - ‎Cited by 33 - ‎Related articles
The fundamental concept underlying the geometry of curves is the arclength of a ..... (a special case of a recent American Mathematical Monthly problem) ...
3. ### [PDF]Elementary Differential Geometry: Curves and Surfaces Martin

by M Raussen - ‎Cited by 2 - ‎Related articles
illustrations of curves and associated objects which are used in the first ... www.math.aau.dk/˜raussen/VIDIGEO/GEOLAB – or by clicking on the figures in.
4. ### [PDF]Curves and Surfaces

by H Schlichtkrull - ‎2011 - ‎Cited by 1 - ‎Related articles
here are curves and surfaces in two- and three-dimensional space, and they are primarily studied ... downloadable from http://www.math.ku.dk/∼thorup/splines/.
5. ### [PDF]Geometry of Algebraic Curves

E-mail address: nasko@math.harvard.edu ... The text for this class is ACGH, Geometry of Algebraic Curves, Volume I. There will be weekly home- works and no ...
6. ### [PDF]A Modern Course on Curves and Surfaces - Department of ...

by RS Palais - ‎Cited by 5 - ‎Related articles
I have taught Math 32 many times since I came to Brandeis in 1960—in fact probably .... in curve and surface theory have very beautiful construcive proofs.
7. ### [PDF]Using Bezier curves for geometric transformations

high school students how geometric transformations could be carried out with ... There are many ways to express a two-dimensional curve mathematically.

8. ### [PDF]and General Helices - Department of Mathematics

by S SY - ‎Cited by 1 - ‎Related articles
of Mathematical Sciences), and Dr. Robert Weidman (Department of Physics), ... basic results of the differential geometry of curves are summarized and ...
9. ### [PDF]GEOMETRIC MODELING: A First Course 4. Curves ... - Usc

Feb 15, 2000 - 4.1 Mathematical Models for Curves and Surfaces. We all have an intuitive ... Figure 4.1.1.2 illustrates the geometry involved. If we denote the ...
10. ### [PDF]Geometric Modelling & Curves - transport@itu.edu.tr

transport.itu.edu.tr/PDF/.../Geometric%20Model%20&%20Curve.pdf
Geometric. Modelling. &. Curves. Geometric Modeling. Creating symbolic models of the physical world has long been a goal of mathematicians, scientists ...
11. ### [PDF]Mathematical Foundation of Geometric Modeling

11/23/06. State Key Lab of CAD&CG. 2. Contents. • Representation of Curves and Surfaces. • Differential Geometry of Curves ...
12. ### [PDF]An Introduction to the Theory of Elliptic Curves - Brown ...

by JH Silverman - ‎2006 - ‎Cited by 6 - ‎Related articles
Jun 19, 2006 - Elliptic curves appear in many diverse areas of math- ematics, ranging from number theory to complex analysis, and from cryptography to ...
13. ### [PDF]MATH 306, Geometry of Curves and Surfaces, Semester 2 ...

https://www.maths.otago.ac.nz/home/.../math306/.../assignment02.pdf?m...
MATH 306, Geometry of Curves and Surfaces, Semester 2, 2014. Assignment 2. Name: due: Wednesday, 23. 7. 2014, 12:00pm. In order to do the assignment ...
14. ### [PDF]I. Classical Differential Geometry of Curves

math.ucr.edu/~res/math138A-2012/dgnotes2012.pdf
This is a first course on the differential geometry of curves and surfaces. ... N. J. Hicks, Notes on differential geometry (Van Nostrand Mathematical Studies No. 3).

### Discrete mathematics related lecture notes

Looking at this 2009 blog:

1. ### [PDF]Discrete Mathematics

Discrete Mathematics. Lecture Notes, Yale University, Spring 1999. L. Lovász and K. Vesztergombi. Parts of these lecture notes are based on. L. Lovász – J.
2. ### [PDF]discrete math lecture notes - Open-source mathematics

opensourcemath.org/books/.../santos-discrete_math_lecture_notes1.pdf
Discrete Mathematics. Mathematics Notes. DiscreteMathematics Notes. Mathematics Notes. DiscreteMathematics Notes. Notes. Discrete MathematicsNotes.
3. ### [PDF]Lecture Notes in Discrete Mathematics - Arkansas Tech ...

Preface. This book is designed for a one semester course in discrete mathematics ... Mathematics is a discipline in which working the problems is essential.
4. ### [PDF]Notes on Discrete Mathematics Miguel A. Lerma

www.math.northwestern.edu/~mlerma/.../discrete_mathematics-2005.pdf
notes will not be completely finished until the end of the quarter. The textbook for this course is Keneth H. Rosen: Discrete Mathe- matics and Its Applications, ...
5. ### [PDF]Discrete Mathematics Lecture Notes Incomplete ... - People

Discrete Mathematics. Lecture Notes. Incomplete Preliminary Version. Instructor: László Babai. Last revision: June 22, 2003. Last update: October 24, 2003 ...
6. ### [PDF]Lecture Notes on Discrete Mathematics - iitk.ac.in

by AK Lal - ‎2012 - ‎Related articles
Sep 26, 2012 - Lecture Notes on Discrete Mathematics. A. K. Lal. September 26 ... We will use the following notation throughout these notes. 1. The empty set ...
7. ### [PDF]Notes on Discrete Mathematics CS 202 - Computer Science

by J Aspnes - ‎Related articles
Oct 24, 2014 - Resources xxii. Lecture schedule xxiv. 1 Introduction. 1. 1.1 So why do I need to learn all this nasty mathematics? . . . . 1. 1.2 But isn't math hard ...
8. ### [PDF]Discrete Mathematics II: Set Theory for Computer Science ...

Feb 10, 2012 - The aim of this part of the 'Discrete Mathematics" course is to introduce ... Sets and logic (Chapter 2; 2 lectures): The basic set operations (union ...
9. ### [PDF]Lecture Notes for College Discrete Mathematics, 2013.

These lecture notes are based on the class material College Discrete Mathe- ... Discrete mathematics deals with the non-continuous mathematics. This.
10. ### [PDF]Discrete Mathematics for Computer Science - University of ...

people.cs.pitt.edu/~milos/courses/cs441/lectures/Class1.pdf
2. M. Hauskrecht. CS 441 Discrete mathematics for CS. Course administrivia. Lectures: • Tuesdays, Thursdays: 11:00 AM - 12:15 PM. • 205 LAWRN. Recitations:.
11. ### [PDF]class notes for discrete mathematics - Abstractmath.org

www.abstractmath.org/MM/dm.pdf
CLASS NOTES FOR DISCRETE MATHEMATICS. NOTE ADDED 14 June 2008. These class notes were used for fifteen years in a discrete math class taught at.
12. ### [PDF]A Course in Discrete Structures - Computer Science

Discrete mathematics deals with objects that come in discrete bundles, e.g., .... We will encounter the following sets and notations throughout the course: • ∅ = { } ...
13. ### [PDF]On the Implementation of a Discrete Mathematics Course

by B Marion - ‎2007 - ‎Cited by 6 - ‎Related articles
Discrete Mathematics Course. Preface. In late 2001, the SIGCSE Board announced a new program, known as the SIGCSE-Committee. Initiative. This program is ...
14. ### [PDF]Discrete Mathematics Lecture #11

Contradiction. • Proof challenge: Establish truth for a large number of propositions. • Key: Adding structure (of different forms) can help make proofs easier.

## Jan 9, 2015

### Mathematics Is Fun: Interesting collections of papers from MAA

The blog page was created in 2011, and I guessed by now the website have gone through (referring to MAA) an overhaul.

Indeed, just take the first item in the old blog:

"[PDF]

### A New Minimization Proof for the Brachistochrone"

And immediately from the first returned link:

[PDF]A New Minimization Proof for the Brachistochrone
by G Lawlor - ‎1996 - ‎Cited by 18 - ‎Related articles
A New Minimization Proof for the Brachistochrone. Gary Lawlor. The American Mathematical Monthly, March 1996

You can see that the link URL has changed.   So if there is any old paper in the old blog that is needed, just enter Google and search again.

Otherwise, since now you now it has been migrated to a entire new directory:

http://www.maa.org/sites/default/files/pdf/pubs/Calc_Articles/ma060.pdf

Therefore, just use Google to start searching from that directory:

This is 1560+ documents (only a snapshot here, and sorry for the HTML formatting error below.   Notice too that only the first link is a valid link, the 2nd link in the each search result's URL is not properly copied over, and I am LAZY):

## Search Results

1. ### [PDF]Sets, Planets, and Comets - Mathematical Association of ...

by M Baker - ‎2013 - ‎Related articles
Sep 6, 2013 - Sets, Planets, and Comets. Author(s): Mark Baker, Jane Beltran, Jason Buell, Brian Conrey, Tom Davis, Brianna. Donaldson, Jeanne ...
2. ### [PDF]February 2008 - Mathematical Association of America

Feb 29, 2008 - 2. MAA FOCUS. February 2008. MAA FOCUS is published by the. Mathematical Association of America in. January, February, March, April, ...
3. ### [PDF]MAA FOCUS - Mathematical Association of America

MAA FOCUS. August/September 2008. MAA FOCUS is published by the. Mathematical Association of America in. January, February, March, April, May/June,.
4. ### [PDF]November 2001 Inside - Mathematical Association of America

Nov 3, 2001 - 2. FOCUS. November 2001. FOCUS is published by the. Mathematical Association of America in. January, February, March, April, May/June,.
1. by FQ Gouvêa - ‎2007
Jan 19, 2007 - FOCUS. January 2007. FOCUS is published by the Mathematical. Association of America in January, February,. March, April, May/June, ...
2. ### [PDF]A Sample Article for Mathematics Magazine - Mathematical ...

A Sample Article for Mathematics Magazine. Jack Q. Firstauthor1. XXXX University. City, State 98765-4321 email@optional.edu. Jill P. Secondauthor.
3. ### [PDF]Kepler's Spheres and Rubik's Cube

by JG PROPP - ‎Cited by 3 - ‎Related articles
May 19, 2014 - Kepler's Spheres and Rubik's Cube. JAMES G. PROPP. University of Maryland. College Park, MD 20742. "How many spheres of radius r may ...
4. ### [PDF]90th Annual Meeting of the MAA - Mathematical Association ...

FOCUS. FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, August/September,. October, November ...
5. ### [PDF]RUBIK'S GROUPS 1. Introduction. Few puzzles have ...

by EC TURNER - ‎Cited by 12 - ‎Related articles
May 19, 2014 - RUBIK'S GROUPS. EDWARD C. TURNER. Department of Mathematics and Statistics, SUNY at Albany, Albany, NY 12222. KAREN F. GOLD.

And this is 7000+ documents (even more), and only a small snapshot shown below:

## Search Results

1. ### [PDF]A Simple Introduction to e - Mathematical Association of ...

2. Édouard Goursat, A course in mathematical analysis, vol. I, Ginn & Co., 1904. 3. C. P. Nicholas, Another look at the probability integral, American ...
2. ### [PDF]classroom capsules - Mathematical Association of America

by MK Kinyon - ‎Related articles
CLASSROOM CAPSULES. EDITOR. Michael K. Kinyon. Indiana University South Bend. South Bend, IN 46634. Classroom Capsules consists primarily of short ...
3. ### [PDF]The Gunfight at the OK Corral

by JT SANDEFUR - ‎Cited by 2 - ‎Related articles
vor. 62, NO. 2, APRIL 1989 119. The Gunfight at the OK Corral. JAMES T. SAN DEFUR. Georgetown University. Washington, DC: 20057. The Movie. The ﬁnal ...
4. ### [PDF]A Fibonacci-like Sequence of Composite Numbers

by DE KNUTH - ‎Cited by 11 - ‎Related articles
A Fibonacci-like Sequence of Composite Numbers. DONALD E. KNUTH*. Stanford University. Stanford, CA 94305. Ronald L. Graham [1] found relatively prime ...
5. ### [PDF]Schur Positivity of Differences of Products of Schur Functions

Schur Positivity of Differences of. Products of Schur Functions. Jeremiah Emidih, University of California Riverside. Nadine Jansen, North Carolina A&T State ...
6. ### [PDF]Sines and Cosines of Angles in Arithmetic Progression

by MP Knapp - ‎2009 - ‎Cited by 9 - ‎Related articles
VOL. 82, NO. 5, DECEMBER 2009. 371. Sines and Cosines of Angles in Arithmetic Progression. MICHAEL P. KNAPP. Loyola University Maryland. Baltimore ...

And so there goes the problem of "404" not found error.   Hopefully the same lesson can apply to all other errors found in these ever-changing web universe.

### Mathematics Olympiad Problems (2015 update)

Or partial results listed here (note that for EACH search result that returned, the first link is the correct link and the 2nd one is incorrect, as the actual content of the url "..." have not been accurately reproduced:

## Search Results

1. ### [PDF]BMO problems from the past - British Mathematical Olympiad

www.bmoc.maths.org/home/bmolot.pdf
students sit a paper with just 3 Olympiad-style problems. The UK Team for this summer's. International Mathematical Olympiad (to be held in Istanbul, Turkey ...
2. ### [PDF]Problem-Solving Strategies: Research Findings from ...

sms.math.nus.edu.sg/.../Problem-solving%20strategies%20-%20research...
tives regarding the nature of mathematics and how one goes about working it). This paper ... Another useful heuristic in solving olympiad problems is to modify.
3. ### [PDF]60-odd YEARS of MOSCOW MATHEMATICAL OLYMPIADS

andrej.fizika.org/ostalo/gimnazija/math/ruske.../11a-olym-1.pdf
the USSR), or the International Olympiad but the problems it offers are on the whole ... great part of the problems offered at Moscow Mathematical Olympiads (an ...
4. ### [PDF]Shortlisted Problems with Solutions - International ...

https://www.imo-official.org/problems/IMO2013SL.pdf
54th International Mathematical Olympiad. Santa Marta ... The Organizing Committee and the Problem Selection Committee of IMO 2013 thank the following.