Prove It: The Art of Mathematical Argument

Rated 4 out of 5 by from Good Review of Proof Approaches; High School Level This is a well-done overview of the variety of ways mathematicians have devised to approach proving mathematical statements. Those who like learning about math for its own sake (this includes me) may find the course inherently interesting. Those studying math at a high school or early college level may gain a helpful extension of their basic understanding. Professor Edwards clearly loves his subject, as his unfailing smile and good humor demonstrate. He generally speaks in short, unadorned sentences, as if any syntactical complexity might impede our understanding of his mathematical points. This approach is also manifest in his frequent use of such comic book exclamations as "Ouch!" and "Wow!". (He is also the first professor I have ever seen actually employ, in real life, the stereotypical lecturer's gesture of touching the fingertips of each hand to each other; very endearing!) A few relatively minor complaints: I very much wish that more time was spent helping us to achieve an intuitive understanding of the abstract math. Venn diagrams, for example, would have been a great help in the early lectures on logic. (They were introduced briefly later.) And while the essential number 'e' is the subject of the entire final lecture, the natural logarithms (logarithms of base 'e') are discussed earlier with no attempt to explain 'e' or why it should be an especially important logarithmic base. There is also frequent and unnecessary repetition of simple points, and sometimes inadequate (at least for me) explanation of some of the more complex ideas. It is also worth noting that the level of the presentation ranges from junior high school to second year college. At times I was bored; at others, working hard to keep up. And I could certainly have done without TGC's annoying sound effects - irritating beeps to emphasize important points. So - I do recommend this course for intermediate-level math aficionados, and for motivated high schoolers. It is unlikely, I think, that you will appreciate each lecture equally, but overall I found it a worthwhile investment of my time.
Date published: 2018-11-04
Rated 5 out of 5 by from Big-time ^ Truly Great Before I bought this course I had had one “very readable book,” which happens to be in this course’s bibliography, and a webpage on four proof techniques. My 30-year-old virtual memories had so eroded, and Dover’s_Real Analysis_is so poorly written that I couldn’t get from one paragraph to the next. Thus began a growling curiosity for the elegance of theoretical math. The first time through the course a few years back, I recall the content as clearer than my Cambridge book, and more thorough and expansive than the webpage, but something essential eluded me. I still couldn’t reason properly in the course’s terms and moved on to other courses, including Prof Grabiner’s Math, Philosophy, and the Real World [#1440], which is paced very slowly but explains the atmosphere of a lot of basic reasoning. (Yes, I agree Prove It is a good step toward Prof Benjamin’s Discrete Mathematics [#1457], which is a barn burner, an artwork to be proud of; and I too would like to see a course on vector calculus and analysis.) The second time through Prove It: The Art of Mathematical Argument (an unfortunate title because most mathematicians “reason” mathematically, and only argue about sports or pizza), with the guidebook, and determined to master again the entirety, it didn’t just survive a second viewing (an ultimate commendation), I was able to see so much deeper into the subject. As a complete physics innumerate, I’m fresh off Physics in Your Life [#1260] by the rapid-fire Prof Wolfson and was at first shocked by the abundance of apparently dead air and the grade-school pace of Lecture One in Prove It. As the metronome clicked at about 30 bpm, I noticed that the very sharply edited new setting and updated production does not necessarily improve the content over older courses with outdated graphics (I’ve learned just as much from the oldest courses as from the most recent). The beauty abundant in this course, though, whether the setting, or Professor Edwards’s colorful neckties (he dresses exceedingly well), is appreciated. Regarding my second time through, a burst of fire here, a sudden movement there, by Lecture Two I was reminded how powerful and serious this man is, touched with the most pleasant humor. He’s excellent with body movement, addressing or gesturing audience stage right while onscreen graphics are moving that way. Indeed, he employs his whole body to transmit these ideas. He is a grandmaster of a teacher. The camera angles are so fine it’s like you’re in his classroom. At age 65 during production, he comes out with the most amazing asides from across his epochal career. By Lecture Five, I began to appreciate the repetition and slow tempo; because by then, from his masterpiece of organization, the whole orchestra was singing. By Lecture Six I was often hitting pause and rewinding, and viewing each subsequent lecture multiple times. (I too find set theory dreadfully onerous, but essential.) By the end of the 24-lecture course—and it’s all Professor Edwards, not multiple professors as mistakenly posted below—I was still challenged and will be going over and over this course every two years for the rest of my life. If you’re into math, I have found gold here and wouldn’t limit in the slightest the set of lifelong learners to whom I would recommend this truly wonderful offering. Thank you, Dr. Edwards, and all behind this exquisite product. This is big-time.
Date published: 2018-10-04
Rated 5 out of 5 by from very full of information Have not had time to finish but am enjoying, as usual, the DVDs. Each teacher has a different perspective and covers something new as in this method of proving math.
Date published: 2017-12-02
Rated 5 out of 5 by from Great Introduction to a "Thick" Subject I'll be taking Discrete Math as an older college student and this course is a great entry point. Professor Edwards's pacing and level of language is good an appropriate. My only criticism is that some of the content, such set theory, is hard to apply to day to day life. I say with some bias because I am studying to be a MS math teacher and I'm always on the look out for real-life connections. It makes the subject come alive.
Date published: 2017-06-26
Rated 1 out of 5 by from Not enough information The classes are too vague. They do not provide the same information that you would take as a comparable college class.
Date published: 2017-06-20
Rated 4 out of 5 by from Quite interesting This is quite interesting and fills in a gap in my knowledge.
Date published: 2017-04-10
Rated 5 out of 5 by from Good Course This is an excellent course. I like the professor style, he's very clear and concise. I couldn't stop watching the first day.
Date published: 2017-04-03
Rated 5 out of 5 by from Great Overview of Proofs First of all, this is one of my favorite courses I've watched so far. The level of mathematics isn't too deep and should be understandable by those with a grasp of Algebra. As a math education major in college, I struggled with proofs. In fact, for many students, proofs are hard to read and hard to do. A high school or college student who is "good" at math may successfully navigate courses like algebra, calculus, only to struggle when they hit a proof-based upper-level math class (e.g., Discrete Math, Linear Algebra). Why? In my experience, students aren't always given a framework of how to think about and do proofs. Professor Edwards gives a nice introduction to the topic that helps take out some of the mystery to doing proofs. He covers some of the types of proofs you'll encounter (e.g., direct proofs, proof by contradiction, and induction). He also gives nice tips like when you encounter a mathematical conjecture you'd like to prove, ask yourself, do you believe it? He encourages you to play around with it and get a feel for it. He encourages you to use scratch paper to work out solutions, i.e., you're not going to get it right the first time! I think the course provides a great foundation and will build confidence in reading and doing proofs. If you're a high school student or college student who will major/minor in a math-related discipline, I would definitely view these lectures...I wish I would have! Then if you'd like to take your study of proofs even further, get a text on proofs (e.g., How to Read and Do Proofs by Solow, or How to Prove It by Velleman); but, you'll find the foundation you got from this set of lectures will make the next level of study more digestible! This course will also provide a nice foundation and help reinforce concepts in other Great Courses math videos, e.g., the Discrete Math course by professor Benjamin (which is a much more math and proof intensive course).
Date published: 2016-10-27
Rated 5 out of 5 by from Very Satisfying Course Mathematical proofs had been my nemesis since honors trig in high school, where we were required to prove a lot of the theorems, but were never given any training on how to do this. Later, as an engineering undergrad student, I wanted to prove the the theorems taught in calculus, differential equations, etc., but I didn't have the time or the training in mathematical proofs so I learned to just hit the "I believe" button. This course gives you a great background in how to do mathematical proofs, using direct proof, induction, contradictions, etc. I would have loved to have had this course available to me in high school or engineering school. This course helped me to correct what I felt was a huge deficiency in my education. Highly recommended for high school or college students studying math, science, or engineering, who haven't been exposed to how to do basic mathematical proofs. Really basic algebra and geometry would be the only prerequisite. Also recommended for those long out of school, for whom mathematical proofs are an intriguing mystery.
Date published: 2016-10-10
Rated 5 out of 5 by from Excellent overview of proofs This is professor Edwards at his best. Just the right mix of theory and practice. This would be great as an intro course but it has enough meat for a good review of proofs even into lower level graduate courses. Professor Edwards has a very easy to listen to manner and a dry sense of humor that should put students at ease.
Date published: 2016-06-25
Rated 5 out of 5 by from I liked very much proving by math induction Wow, this is a beautiful math course given by a beautiful mind. During my first year of college I was scared of mathematical induction. I always wanted to learn about this powerful math methodology. Professor Edwards is an excellent teacher, He included 3 beautiful lectures regarding this topic. In addition, the lectures about mathematical logic are outstanding. The entire course is very valuable. I would like to ask the Teaching Company to consider a new course on Linear Algebra by Professor Edwards to complement his other excellent courses on Pre-calculus and Calculus.
Date published: 2016-03-30
Rated 5 out of 5 by from Prove it An invigorating course superbly taught and presented. Excellent graphics. Highly recommended.
Date published: 2015-10-06
Rated 5 out of 5 by from Not so esoteric If you are interested in math or science and then this is a must. If you have to take math and don't like it, then this course will help unlock math's mysteries. If you're interested in being a business leader or a leader in general this course will help you in most needed critical thinking skills. The professor is excellent so good in fact that I took two more courses of his.
Date published: 2015-02-10
Rated 4 out of 5 by from Prove It prove its value I am only in the first part of this course but I am impressed with the simplicity with which it is presented. So far everything has been of great interest. The only fault so far has been in the editing. In the first lecture, after describing the Pythagorean theorem they present an illustration of a right triangle and label the sides x2, y2 and z2. If these are real numbers then Fermat's final theorem would be false. The sides should have been labeled x, y, and z. Once they are squared they will no longer make a triangle.
Date published: 2015-01-12
Rated 5 out of 5 by from Great Course. Awesome Professor. I really enjoyed watching all of the lectures. The professor really made this subject approachable and interesting. His genuine, down-to-earth presentation of the subject makes the content less intimidating and easier to understand. The pace is very good and each lecture logically builds on the previous one. I purchased the Calculus courses taught by Professor Edwards solely based on how well this material was presented.
Date published: 2014-12-24
Rated 5 out of 5 by from Excellent Course Many years ago I studied physics; therefore, I am familiar with the topic of the advanced math. From my perspective, this course inspires me to rethink about some of my understanding of the topics in mathematic that I have learned in the past. I strongly recommend this course to students of physics, engineering, and philosophy.
Date published: 2014-11-13
Rated 5 out of 5 by from fun course Lots of fun whether you are a technical type or have nothing more than a good facility with algebra. The many methods of mathematical proofs were very well described by this excellent teacher. He has the style of your favorite grandfather; smart but not condescending. There is mathematical 'elegance' in proving the inner workings of even seemingly simple algorithms.
Date published: 2014-03-17
Rated 2 out of 5 by from Mathemata mathematicis propter If one of your personal mottoes is: "Mathemata mathematicis propter" then this course is for you. While viewing these lectures, I finally began to understand why I have difficulty, even disdain, for maths. I have little to no appreciation for the “beauty” or “elegance” in the art of maths. Admittedly, I have rarely had the affect of the genius of any creative art. In other words, no art really “speaks” to me. My loss.... Perhaps others will find this course enlightening. Algebra and algebra-er.... This is the first course in my Teaching Company courses library that didn’t motivate me to want to study further. Not so much that it's boring, but, for me, thin on practicality. Should be titled: A Closer Look at Algebra. This could be a good course for algebra lovers. Otherwise, I had no applicable use for this topic. No offense to Professor Edwards or to the good people at the Teaching Company. With this course, I have proven to myself that I just don't like math. In the famous words of Professor Devadoss, “Who cares?”.
Date published: 2013-12-25
Rated 5 out of 5 by from A Course that Lives Up to the Company Name This DVD really lives up to the company name. It is a great course! Professor Edwards has an excellent presentation and the video complements the topics perfectly. While watching these DVDs, I have also been taking Kevin Devlin’s Coursera Course “Introduction to Mathematical Thinking.” Both course cover a lot of the same material, but “Prove It” is far superior. Not only is it visually superior, but Edwards explanations are short and to the point. I would guess I get four or five times as much knowledge per hour from Edwards’ course.
Date published: 2013-10-24
Rated 5 out of 5 by from Fun and fruitful I love this course! I took some proof-based classes as an undergraduate, and I am a pretty hardcore user of mathematics in my profession. It has been a while since I sat down to prove anything, and I started plenty rusty. I left feeling ready to tackle new things. This course requires active participation to get the most out of it. Dr. Edwards is a great teacher, and guides one through the thickets, gently but with plenty of challenges. I had a pad of paper in my hands the whole time, and he mentioned things that I later went and looked for on the internet. If you are new to proofs, this is a good choice, and if you have done proofs, but long ago, it is a great refresher. This was my first TGC purchase, but will certainly not be my last.
Date published: 2013-09-08
Rated 5 out of 5 by from Most Enjoyable Course Dr. Edwards is a masterful professor. All of the subjects that are covered in this course are understandable to anyone who has moderate mathematical maturity. To those students who are interested in learning more, or (like myself) want a refresher in one’s knowledge of problem-solving, this is an excellent course. Each lecture contains pertinent examples that illustrate the technique of each proof, and where solutions have yet to be discovered, Dr. Edwards suggests unsolved problems that the student might choose to pursue. As a mathematician myself, I would highly recommend this course to anyone who is interested in the fine art of mathematical proofs and solution techniques.
Date published: 2013-07-17
Rated 5 out of 5 by from A Truly Great Course. I am amazed at how this course was put together. Excellent use of technology paired with examples. This makes the material easy to follow and retain. Professor Edwards is well paced for the learner. He never rushes anything and is clear before moving forward. I highly recommend any of his courses. I hope he can continue to produce higher mathematics courses. This guy is a living example of great teaching.
Date published: 2013-05-07
Rated 5 out of 5 by from One of the Best in the Catalog I wish I had had this course when I was a full time student. This is simply the best course I have seen on a math topic and it is one of the best in the Teaching Company's collection. This course is incredibly useful in giving the background on proofs that simply does not exist in general math books and is impossibly dry in books on proofs. I cannot recommend this too highly.
Date published: 2013-04-06
Rated 5 out of 5 by from Excellent and highly recommended Great content, very interesting, and well presented by a really outstanding and highly engaging instructor. Highly recommended. A fun course!
Date published: 2013-03-25
Rated 5 out of 5 by from Prove it As usual professor Edwards is excellent. Great presentation of complex ideas and concepts. Clear definition with examples that "prove" the subject under discussion. To those that like Mathematics, this course will answer many "why's" and will provide the insights to proofs that unfortunately were not provided in College. I encourage The Great Courses company and Professor Edwards to expand the subjects offered in these courses like, Non-Euclidean Geometry, Advance Calculus or the like. More Problems at the end of each chapter, of the Guidebook will help consolidating the concepts learned during the lecture. "Prove it" is a great course.
Date published: 2013-01-01
Rated 5 out of 5 by from Great intro to mathematical proof and more Mathematical reasoning, and mathematical proof, is where high school math turns into college math. Having enjoyed Professor Edwards' other TC courses on high school level calculus and precalculus I was looking forward to his new course on Mathematical Argument, and he did not disappoint. Although maybe Professor Edwards' style of presenting is more perfectly suited for a high school level course, he managed to keep this new course interesting from beginning to end. He obviously loves math, and it is difficult not to get infected with his enthusiasm when another theorem gets proved properly in this course. In addition to the lessons that deal strictly with mathematical proof and argument, this course also begins to give an introduction to number theory, making me look forward to yet another TC course out there...
Date published: 2012-11-09
Rated 5 out of 5 by from You Too Can "Prove It." Let me begin by stating I’m a retired mathematics instructor who had a very successful and rewarding career of 39 years and I actually used the PreCalculus and Calculus textbooks, which I thought were the best available, written by Dr. Edwards and his coauthors. In “Prove It: The Art of Mathematical Argument” Professor Edwards shows why mathematical proof is indeed the gold standard of knowledge. He leads you on a thought-provoking journey that allows you see beyond the “how” to do mathematics into the realm of “why” mathematical statements are true. After illustrating the basic principles of logic, he proceeds to show you the abstract order behind all things. He uses many techniques including direct proof, proof by contradiction, induction, and visual proof. Like his previous Great Courses, Dr. Edwards’ presentation is logical and clear. His carefully chosen examples are insightful and illuminating. His pleasant and enthusiastic style keeps the course moving in an interesting and educational manner. By the end of the course you will have experienced the thrill of understanding proofs and actually constructing your own. Lest you begin to conclude all things have been proven, Professor Edwards also talks about many unproven conjectures that illustrate the never-ending and exciting quest to “prove it”. WARNING: Mathematics is not a spectator subject; you cannot just listen to an instructor, no matter how good he might be, but must actually work out examples yourself in order to find and correct mistakes that may be unique to you. It takes practice along with an excellent instructor to guarantee success; therefore, I highly recommend you work out the additional practice problems given in the accompanying guidebook in order to help you gain confidence and mastery of this challenging, satisfying, and important skill. This course could change your attitude toward mathematics and is highly recommended.
Date published: 2012-10-26
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Prove It: The Art of Mathematical Argument
Course Trailer
What Are Proofs, and How Do I Do Them?
1: What Are Proofs, and How Do I Do Them?

Start by proving that two odd numbers multiplied together always give an odd number. Next, look ahead at some of the intriguing proofs you will encounter in the course. Then explore the characteristics of a proof and tips for improving your skill at proving mathematical theorems.

32 min
The Root of Proof-A Brief Look at Geometry
2: The Root of Proof-A Brief Look at Geometry

The model for modern mathematical thinking was forged 2,300 years ago in Euclid's Elements. Prove three of Euclid's theorems and investigate his famous fifth postulate dealing with parallel lines. Also, learn how proofs are important in Professor Edwards's own research.

31 min
The Building Blocks-Introduction to Logic
3: The Building Blocks-Introduction to Logic

Logic is the foundation of mathematical proofs. In the first of three lectures on logic, study the connectors "and" and "or." When used in combination in mathematical statements, these simple terms can create interesting complexity. See how truth tables are very useful for determining when such statements are true or false.

30 min
More Blocks-Negations and Implications
4: More Blocks-Negations and Implications

Continue your study of logic by looking at negations of statements and the logical operation called implication, which is used in most mathematical theorems. Professor Edwards opens the lecture with a fascinating example of the implication of a false hypothesis that appears to pose a logical puzzle.

30 min
Existence and Uniqueness-Quantifiers
5: Existence and Uniqueness-Quantifiers

In the final lecture on logic, explore the quantifiers "for all" and "there exists," learning how these operations are negated. Quantifiers play a large role in calculus-for example, when defining the concept of a sequence, which you study in greater detail in upcoming lectures.

30 min
The Simplest Road-Direct Proofs
6: The Simplest Road-Direct Proofs

Begin a series of lectures on different proof techniques by looking at direct proofs, which make straightforward use of a hypothesis to arrive at a conclusion. Try several examples, including proofs involving division and inequalities. Then learn tricks that mathematicians use to make proofs easier than they look.

31 min
Let's Go Backward-Proofs by Contradiction
7: Let's Go Backward-Proofs by Contradiction

Probe the power of one of the most popular techniques for proving theorems-proof by contradiction. Begin by constructing a truth table for the contrapositive. Then work up to Euclid's famous proof that answers the question: Can the square root of 2 be expressed as a fraction?

31 min
Let's Go Both Ways-If-and-Only-If Proofs
8: Let's Go Both Ways-If-and-Only-If Proofs

Start with the simple case of an isosceles triangle, defined as having two equal sides or two equal angles. Discover that equal sides and equal angles apply to all isosceles triangles and are an example of an "if-and-only-if" theorem, which occurs throughout mathematics.

31 min
The Language of Mathematics-Set Theory
9: The Language of Mathematics-Set Theory

Explore elementary set theory, learning the concepts and notation that allow manipulation of sets, their unions, their intersections, and their complements. Then try your hand at proving that two sets are equal, which involves showing that each is a subset of the other.

30 min
Bigger and Bigger Sets-Infinite Sets
10: Bigger and Bigger Sets-Infinite Sets

Tackle infinite sets, which pose fascinating paradoxes. For example, the set of integers is a subset of the set of rational numbers, and yet there is a one-to-one correspondence between them. Explore other properties of infinite sets, proving that the real numbers between 0 and 1 are uncountable.

32 min
Mathematical Induction
11: Mathematical Induction

In the first of three lectures on mathematical induction, try out this powerful tool for proving theorems about the positive integers. See how an inductive proof is like knocking over a row of dominos: Once the base case pushes over a second case, then by induction all cases fall.

31 min
Deeper and Deeper-More Induction
12: Deeper and Deeper-More Induction

What does the decimal 0.99999... forever equal? Is it less than 1? Or does it equal 1? Apply mathematical induction to geometric series to find the solution. Also use induction to find the formulas for other series, including factorials, which are denoted by an integer followed by the "!" sign.

31 min
Strong Induction and the Fibonacci Numbers
13: Strong Induction and the Fibonacci Numbers

Use a technique called strong induction to prove an elementary theorem about prime numbers. Next, apply strong induction to the famous Fibonacci sequence, verifying the Binet formula, which can specify any number in the sequence. Test the formula by finding the 21-digit-long 100th Fibonacci number.

30 min
I Exist Therefore I Am-Existence Proofs
14: I Exist Therefore I Am-Existence Proofs

Analyze existence proofs, which show that a mathematical object must exist, even if the actual object remains unknown. Close with an elegant and subtle argument proving that there exists an irrational number raised to an irrational power, and the result is a rational number.

31 min
I Am One of a Kind-Uniqueness Proofs
15: I Am One of a Kind-Uniqueness Proofs

How do you prove that a given mathematical result is unique? Assume that more than one solution exists and then see if there is a contradiction. Use this technique to prove several theorems, including the important division algorithm from arithmetic.

31 min
Let Me Count the Ways-Enumeration Proofs
16: Let Me Count the Ways-Enumeration Proofs

The famous Four Color theorem, dealing with the minimum number of colors needed to distinguish adjacent regions on a map with different colors, was finally proved by a brute force technique called enumeration of cases. Learn how this approach works and why mathematicians dislike it-although they often rely on it.

31 min
Not True! Counterexamples and Paradoxes
17: Not True! Counterexamples and Paradoxes

You've studied proofs. How about disproofs? How do you show that a conjecture is false? Experience the fun of finding counterexamples. Then explore some famous paradoxes in mathematics, including Bertrand Russell's barber paradox, which shook the foundations of set theory.

30 min
When 1 = 2-False Proofs
18: When 1 = 2-False Proofs

Strengthen your appreciation for good proofs by looking at bad proofs, including common errors that students make such as dividing by 0 and circular reasoning. Then survey the history of attempts to prove some renowned conjectures from geometry and number theory.

31 min
A Picture Says It All-Visual Proofs
19: A Picture Says It All-Visual Proofs

Before he became the 20th U. S. president, James A. Garfield published an original proof of the Pythagorean theorem that relied on a visual argument. See how pictures play an important role in understanding why a particular mathematical statement may be true. But is a visual proof really a proof?

32 min
The Queen of Mathematics-Number Theory
20: The Queen of Mathematics-Number Theory

The great mathematician Carl Friedrich Gauss once said that if mathematics is the queen of the sciences, then number theory is the queen of mathematics. Embark on the study of this fascinating discipline by proving theorems about prime numbers.

29 min
Primal Studies-More Number Theory
21: Primal Studies-More Number Theory

Dig deeper into prime numbers and number theory by proving a conjecture that asserts that there are arbitrarily large gaps between successive prime numbers. Then turn to some celebrated conjectures in number theory, which are easy to state but which have withstood all attempts to prove them.

31 min
Fun with Triangular and Square Numbers
22: Fun with Triangular and Square Numbers

Use different proof techniques to explore square and triangular numbers. Square numbers are numbers such as 1, 4, 9, and 16 that are the squares of integers. Triangular numbers represent the total dots needed to form an equilateral triangle, such as 1, 3, 6, and 10.

30 min
Perfect Numbers and Mersenne Primes
23: Perfect Numbers and Mersenne Primes

Investigate the intriguing link between perfect numbers and Mersenne primes. A number is perfect if it equals the sum of all its divisors, excluding itself. Mersenne primes are prime numbers that are one less than a power of 2. Oddly, the known examples of both classes of numbers are 47.

31 min
Let's Wrap It Up-The Number e
24: Let's Wrap It Up-The Number e

Prove some properties of the celebrated number e, the base of the natural logarithm, which plays a crucial role in precalculus and calculus. Close with a challenging proof testing whether e is rational or irrational-just as you did with the square root of 2 in Lecture 7.

32 min
Bruce H. Edwards

I love mathematics and tried to communicate this passion to others, regardless of their mathematical backgrounds.


Dartmouth College


University of Florida

About Bruce H. Edwards

Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogota, Colombia, as a Peace Corps volunteer. Professor Edwards has won many teaching awards at the University of Florida, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991-1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of mathematics textbooks with Professor Ron Larson. Their textbooks have been honored with various awards from the Text and Academic Authors Association.

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