1996 putnam exam pdf

The fiftyseventh annual william lowell putnam mathematical competition. The william lowell putnam competition is held annually for the. A triangle abc has h as the intersection of the altitudes, o the center of the circumscribed circle, m the midpoint of bc,andf the foot of the altitude from a. The putnam competition takes place annually on the first saturday of december. The william lowell putnam mathematics competition is a north american math contest for college students, organized by the mathematical association of america maa. We induct on nwith the base case n 1 already given. Learn more about our competitions and resources here. First suppose we are in the following situation for some k. An examination of research on contemporary professional development suzanne m. Prove that if n1 an is a convergent series of positive real numbers, then so. What is the best way to prepare for the putnam competition. Then t 1t 2u 1u 2 2u while t 1t 2u 1u 22t, contradiction. Congratulations to harvards team of sehun kim 22, sheldon kieran tan 23 and franklyn wang 22 for placing second among 570 institutions in the united states and canada competing in the exam. The remaining solutions are modi ed versions of these or originals by dennis.

Hilary putnam, who may have been the first philosopher to advance the notion that the computer is an apt model for the mind, takes a radically new view of. William lowell putnam mathematical competition, 19852000, problems. Let and be the angles at the vertices aand b, respectively. The william lowell putnam mathematical competition is the preeminent mathematics competition for undergraduate college students in the united states and canada. The william lowell putnam mathematical competition. Vakil, the william lowell putnam mathematical competition.

A1 find the least number a such that for any two squares of. Develops the equivalent of a graduate level course in classical analysis real and complex based on problem solving. Each year on the first saturday in december, several thousand us and canadian students spend 6 hours in two sittings trying to solve 12 problems. In the triangle abc, let gbe the centroid, and let ibe the center of the inscribed circle. Problems intended to be a1 or b1 and therefore relatively easy are marked accordingly. Suppose that a, b, c, and dare distinct points, no three of which lie on a line, in the euclidean plane. Fiftyseventh annual william lo well putnam ma thema tical competition saturda y, decem b er 7, 1996 examination a a1. William lowell putnam mathematical competition wikipedia. Teacher learning and the acquisition of professional. The william lowell putnam mathematical competition, often abbreviated to putnam competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the united states and canada regardless of the students nationalities. Solutions to the 71st william lowell putnam mathematical co mpetition saturday, december 4, 2010 kiran kedlaya and lenny ng a1 the largest such k is.

Putnam and beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. The 53rd william lowell putnam mathematical competition. It consists of two threehour sessions in each of which six problems are given to be. Thewilliamlowellputnam mathematicalcompetition 19852000. Solutions to the 57th william lowell putnam mathematical competition. Solutions to the 56th william lowell putnam mathematical. Let us make clear from the start that we have not tried with this collection to imitate the scholarly and extensive treatment of the first twentyfive contests by gleason, greenwood, and kelly the william lowell putnam mathematical competitionproblems and solutions. Pdf the william lowell putnam mathematical competition 1985. This work may be used as a study guide for the putnam exam, as a text for many different problemsolving courses, and as a source of problems for standard courses in undergraduate mathematics. Find the least n um b er a suc h that for an y t w o squares of com bined area 1, a rectangle of area a exists suc h that the t w o squares can b e pac k ed in the rectangle without in terior o v erlap. Show that if the squares of the lengths of the line segments ab, ac, ad, bc, bd, and. The 57th william lowell putnam mathematical competition.

Solutions to the 56th william lowell putnam mathematical competition saturday, december 2, 1995 kiran kedlaya a1 suppose on the contrary that there exist t 1. The american mathematics competitions are a series of examinations and curriculum materials that build problemsolving skills and mathematical knowledge in middle and high school students. Solutions to the 71st william lowell putnam mathematical. Readings mathematical problem solving putnam seminar. Special congratulations to ravi jagadeesan freshman for being a putnam fellow a topsix finisher in the individual competition. Let r be the region in the first quadrant bounded by the yaxis, the line y mx, and the ellipse.

The competition consists of two 3hour sessions, one in the morning and one in the afternoon. While many of the problems are too sophisticated for contests such as the putnam exam, there are still a large number of more accessible problems covering material almost impossible to learn otherwise. Feel free to see me or email me if you need a hint, or if you think you have a solution and want to check it 1. It is not about the history of the competition, the. Find the least number a such that for any two squares of combined area 1. Putnam and other problems sorted according to topic university of. The problems marked with asterisks actually appeared on the putnam exam possibly reworded. Solutions to putnam exam problems for 1 dec 2001 prof. At most schools, 10 students show up for the prestigious math competition. Putnam and beyond is organized for independent study by undergraduate and graduate students.

Congratulations once again to our team members and outstanding individuals in this years putnam competition. Results from the 2019 competition, held on saturday, december 7, are now posted. The william lowell putnam mathematical competition, often abbreviated to putnam. Then the shorter side of a rectangle containing both squares without overlap must be. I coached caltechs putnam team when i was a graduate student. The putnam competition from 193820 university of minnesota. The william lowell putnam mathematical competition 19852000. Putnam competition mathematical association of america. Wilson and jennifer berne michigan state university in the past 10 years, the calls for a commitment to teacher learning have increased exponentially, most likely from a confluence of forces.

William lowell putnam mathematical competition past problem sets. The first 5 competitions had a total of 77 problems, the next 17 had 14 each, and the last 41 thru 2002 had 12 each. The putnam competition is an exam that is given to the finest undergraduate math students all over the united states, sponsored by the mathematical association of america usually between 2,000 and 3,000 students enter the competition each year. Li hong kong mathematical society international mathematical olympiad hong kong committee supported by the quality education fund. Let f n and g n be the polynomials in the induction hypothesis and let u h f ng n 0 mod pn. The 75th annual putnam exam took place on saturday, december 6, 2014.