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22
The nicest math book I own
By Antonio Cangiano. Filed under Suggested reading | 9 Comments
I recently got a hold of what I consider to be the nicest mathematical book in my collection. As a matter of fact, it’s the nicest book I own, period - even though I posses bookshelves teaming with terrific titles on mathematics, science, programming, computer science, photography and so on. The book I’m talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this title. You don’t have to click on the link with my referral if you don’t want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight.
I’d like to claim that I’ve read it cover to cover. But I haven’t. At 1014 pages (and a hefty five and a half pounds), this recently published hardcover tome will probably take me a while to properly read through in its entirety. It can serve as a reference that can be randomly accessed if you so chose, but from what I’ve read so far, I’m extremely impressed and am eager to pursue my way through it systematically. It will be time really well spent, and dare I say, a life changing experience. This is the book to bring on a proverbial desert island, if you were allowed only one title.
The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it’s a monumental piece of work. I have never seen a book like this before. It rigorously illustrates the (pure) mathematical field while remaining as accessible as possible to the general reader. There is no mathematician in the world who, upon reading this book cover to cover, would not have learned a great deal from it. And I’m sure this includes Timothy Gowers himself, who was the book’s Chief Editor and who brilliantly managed to coordinate a team of world class experts to cover (again in an accessible manner) their respective fields of expertise. Such experts not only are the best mathematicians alive today in their respective areas of expertise, but are also absolutely wonderful teachers who have the uncanny ability to divulge information in a understandable manner, under the editorial guidance of Professor Gowers. Timothy Gowers, by the way, also has a blog, which contains discussions about the book and a helpful errata.
This book is what I now consider to be the bible of mathematics, and unlike a typical reference or encyclopedia, The Princeton Companion to Mathematics never fails to provide a sense of unity and cohesion, both of which are essential if you want to truly provide an (nearly) complete panorama of a subject. While all the basics are well explained with the clarity and simplicity of really good popular science, this tome doesn’t skimp on details or theorems when it comes to highly advanced topics that few people are familiar with. The style remains geared towards providing a good introduction to each subject, as opposed to a PhD thesis, and as such it will prove useful to the ambitious high school student, as well as professional mathematicians or graduate students. And as if all this wasn’t enough, they managed to squeeze in a biographical overview of the most important historical mathematicians from Pythagoras to Bourbaki, as well as a respectable (yet not overly comprehensive section) about applied mathematics, and math’s influence on other disciplines.
I believe this is the kind of book that will still be is use a hundred years from now, even though by then it will be slightly outdated. This title is destined to be fully revered as a classic and monumental review of the subject of pure mathematics. I salivate like Pavlov’s dogs at the idea of the amount of fun I will have exploring this book, which will no doubt expose my ignorance about several key areas of math, and yet at the same time help me to remedy such things.
This Christmas, give yourself a great gift and get this book. If you are looking for the perfect gift for people who’re interested in mathematics, this is the right book. If your are a parent, I especially encourage you to pick it up for your son or daughter, it could change their lives. Ladies, your geeky boyfriend will likely propose to you if you put a copy under the tree. Jokes aside, The Princeton Companion to Mathematics makes for a great read to start 2009 off with.
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Oct
24
Blogging in Math Class
By Katherine Stange. Filed under Math Education, Math Websites | 1 Comment
I’m hip-deep in the teaching of Mathematics 152, a discrete mathematics course titled “The Mathematics of Symmetry” designed by Paul Bamberg and taught at Harvard University. The course is seminar-style: the students take turns presenting the material in 5-to-15-minute assigned topics during class. The design puts an emphasis on learning to communicate mathematics, and so as I took over the course this semester I considered what I might do to further this goal. I wanted to encourage class participation, discussion and a sense of community, as well as tie the mathematics of the course to the wider experience of the students. So I tried an experiment: an assigned community math blog. The blog is open to and in fact aimed at the layperson public, but also serves as a community discussion board for the students. The 23 students in the class have been assigned 4 posting dates each, spread throughout the semester, which means the blog is updated at least once and sometimes twice a day.
I was inspired by my mother and father, who both assign “journals” to their students in psychology, english, classics and philosophy. The journals, updated regularly by students, are a sort of private diary of reactions to the course. They serve to draw connections with the sudents’ world outside the classroom, and encourage reflection on the material. Blogging, it occurred to me, is a sort of public journaling, and provide some of what my parents sought from the course journals, but this time in the form of a community project.
We’re now approaching the halfway mark for the semester, and I’ve been incredibly impressed with the students’ posts. They range from amusing to historical to musical to magical—even social commentary. There’s been no shortage of topic ideas, although I had hoped there would be more discussion via comments. I hope you’ll take a look at the blog and post some responses, so the students see that they are really reaching an audience out there on the internet: reaching beyond the course itself.
Site: The Math 152 Weblog.
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Sep
28
10 Remarkable Female Mathematicians
By Jessica Cangiano. Filed under History, Suggested reading | 8 Comments
Pythagoras, Euler, and G.H. Hardy, if you’re interested in math or if you paid attention in school, chances are you’ve heard of these famous names and may be familiar with their work and accomplishments. But how about Agnesi, Cartwright or Goldwasser? These three names are amongst ten that we’ve selected as a means of highlighting some of the best and brightest female mathematicians of all time; women who unlike their male counterparts, have not always received the same level of recognition even though their achievements and contributions to the world of mathematics are just as important. These women were often groundbreakers, highly determined and very dedicated. They are shining examples of the fact that mathematics is not a “boys only” club, even if at many points in time it’s appeared that way on the surface. Today their work is recognized and appreciated, and they stand as fantastic sources of inspiration for a new generation of students and math enthusiasts – both female and male.
Hypatia of Alexandria (AD 350 to 370 – 415): Born nearly 17 centuries ago, Hypatia of Alexandria was a brazen, highly intelligent woman who excelled in the fields of science, math and philosophy, which at the time (and for hundreds upon hundreds of years further) were seen squarely as the domain of men. Hypatia’s foremost teacher was her father, Theon Alexandricus, a mathematician and philosopher, who she would later go on to contribute to several mathematical works with. Hypatia herself was a teacher, as well as being the inventor of the hydrometer. Though she forged ahead in a time when women were all but ignored in the realm of mathematics, this bright Greek woman eventually met with a tragic death when her chariot was attacked and she was brutally murdered by a gang of Christians. Though her life was cut short, while she was alive, through her accomplishments, Hypatia was able lay the groundwork for future female pioneers of mathematics.
Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet (December 17, 1706 – September 10, 1749): A woman of many intellectual interests, Émilie was a mathematician, author, and physicist who hailed from France. Born into a well-to-do family, Châtelet was a gifted child with a natural penchant for linguistics. Given her family’s high social status, Émilie was able to receive a degree of education far above the vast majority of French women at the time. Her place in society also put her in a position wherein she was able to mingle with some of the leading minds of her time (such as Voltarie, who would go onto become one of her lovers). In 1740, Châtelet published a book entitled Institutions de Physique, which put forth some of her knowledge regarding both science and philosophy. In her last year of life, Émilie translated Newton’s well-known Principia Mathematica. In her early forties she became pregnant, and though she initially survived the pregnancy, a few days later both she and her newborn child passed away. Émilie was an independent, articulate and highly intelligent woman, who was somehow able to hold down both her role as a leading lady in French high society and as a mathematician, an equation which deserves respect in its own right.
Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799): A woman of many skills, Agnesi was an Italian mathematician, linguist, and philosopher whose profound intelligence was evident from an early age. Born into a wealthy and large family (due in part to siblings which sprang from her father’s two subsequent marriages after Maria’s mother passed away), Agnesi was a devoted and studious woman who would go onto publish the first book that dealt with both integral and differential calculus. In 1750, Maria was appointed as chair of mathematics and natural philosophy at the Bologna Academy of Sciences, an incredible accomplishment for any woman in the mid eighteenth century, when exceptionally few universities in Europe allowed women to study, let alone hold teaching positions. Later in life, Agnesi, a deeply religious woman, joined a nunnery and ended her days tending to the less fortunate.
Marie-Sophie Germain (April 1, 1776 – June 27, 1831): Parisian born Germain was a passionate mathematician with a love of number theory and differential geometry. During her lifetime (which, in the context of both France and Europe in general, was a highly tumultuous era) Germain often corresponded under a pseudonym (Monsieur Le Blanc) as a means of hiding her gender when writing to leading male mathematicians of the time such as Lagrange and Gauss. In 1816 Sophie won a contest that was held by the French Academy of Science which dealt with the area of vibrations on elastic surfaces, that in turn lead her to become the first woman (short of some of the staffs’ wives) to attend classes at the Academy. In 1831, the University of Gottengen bestowed an honorary degree to Germain, however she died as a result of breast cancer before she was able to receive the degree. A self-taught mathematician who came of age during a truly unstable period in French history, Sophie will long be remembered for her mathematical contributions in the field of number theory.
Augusta Ada Byron King, Countess of Lovelace (December 10, 1815 – November 27, 1852): English born Ada was the daughter of famed poet Lord Byron, though he was not active in his daughter’s life. Aside from her famous father, Ada is primarily known for her programming work regarding Charles Babbage’s invention of the analytical engine, a very early mechanical general-purpose computer. Lovelace was ahead of her time in this field, as she believed that computers held the capacity to do more than just simply act as calculators. Like many of the women in this list, Ada met with an early death; she was only 36 when she died due to uterine cancer. Today Lovelace is remembered fondly as the first female computer programmer (in era before the modern computer came into existence), and the programming language Ada was named in her honor.
Sofia Vasilyevna Kovalevskaya (January 15, 1850 – February 10, 1891): Generally acknowledged as the first well-known Russian female mathematician, Kovalevskaya (portrayed above) began teaching herself advanced mathematics as a young teen, before going on to leave Russia so that she could attend university in mainland Europe (something that women were not allowed to do in Russia at the time). A very bright, quite and gentle person, Sofia loved to learn and was eager to share this passion with others by teaching math, though this proved to be very challenging for a woman in nineteenth century Russian and Kovalevskaya would again have to leave her homeland so as to take up a position lecturing at the University of Stockholm. Prior to her relatively young passing due to pneumonia, Kovalevskaya published numerous papers on topics pertaining to mathematics and mathematical physics, and won a prestigious award (the Prix Bordin) from the French Academy of Sciences. (Here you can find a mathematical book about her work.)
Amalie Emmy Noether (March 23, 1882 – April 14, 1935): Considered by Einstein to be most important woman in history of mathematics, Emmy (as she generally went by) was an early twentieth century German mathematician with a passion for such areas as theoretical physics and abstract algebra. Noether was both an accomplished university professor and a prolific writer of mathematical papers, as well as someone with a profound ability to grasp abstract thought. As the Nazi stronghold grew in Germany during the 1930s, Emmy found herself, like so many other Jewish professors, barred from teaching. Towards the end of 1933, Noether was able to escape Germany and take up a position at the American college of Bryn Mawr. However, sadly, two years later Emmy’s life was cut short when she died just days after undergoing surgery. To this day Noether’s many contributions towards mathematics and theoretical physics are highly revered, and many remain relevant to the math of the twenty-first century.
Dame Mary Lucy Cartwright (December 17, 1900 – April 3, 1998): An accomplished British mathematician, Cartwright led a long and distinguished career that focused on function theory. In her lifetime, Mary published in excess of 100 papers and was the first female mathematician to be elected as a Fellow of the Royal Society of England; a theorem regarding analytical function that she put forth, Cartwright’s theorem, shares her name. Cartwright received numerous awards and recognitions throughout her life including, the De Morgan Medal of the London Mathematical Society and the Sylvester Medal of the Royal Society.
Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985): An American mathematician who was born in St. Louis, Robinson is known for her work regarding Hilbert’s tenth problem and the field of decision problems. Though plagued by health problems for most of her life, Julia didn’t let this stand in the way of her love of math and the pursuit of knowledge. She taught as a professor at Berkley and was the first female mathematician to be elected to the National Academy of Sciences. An historical first in her career included becoming president of the American Mathematical Society. She would also go on to become elected to the American Academy of Arts and Sciences in the mid 1980s, just a few short years before she passed away from leukemia.
Shafi Goldwasser (b.1958 –): A native of New York (and the only living mathematician on our list), Goldwasser is both a professor of mathematics (at the Weizmann Institute of Science) and of computer science (at MIT, where she was the first person to hold an RSA Professorship). Shafi’s research focuses on areas such as cryptography, complexity theory and computation number theory, and she is well-known for her work with zero-knowledge proofs. For her work in the field of complexity theory, Goldwasser was awarded the Gödel Prize in theoretical computer science twice (1993 and 2001, respectively).
In this article we’ve taken a gander at ten well known and highly esteemed female mathematicians, but the list doesn’t stop here. Throughout history there have been numerous other women whose contributions to the field of mathematics have made significant impacts. In 1971 the Association for Women in Mathematics was formed with the intent of helping to establish and promote equal opportunities and treatment for girls and women in all areas of mathematics, while at the same time helping to encourage more to get involved with math.
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