1 comments about Master Math: Geometry (Master Math Series).

1. The best presentation of geometry I have ever seen. The topics are presented in a logical manner so that they build, are in context, and make sense. It explains logic and proofs in a way students can really understand. Definitions are provided in the beginning so you can orient yourself and understand the jargon of geometry from the start. It presents concepts three ways: a description, a picture, and a description of the picture. It makes learning so easy! There are plenty of real-world and fun examples and tidbits of information that makes learning fun. It is clear, concise, and the topics have a flow and context that makes is easier to learn the material whether you are taking geometry for the first time, are older and need a review, or are taking higher level math, science or engineering classes and need to quickly look something up and understand it. Learning geometry does not need to be a frustrating experience! Everything you need for basic geometry is in this book! Master Math: Basic Math and Pre-Algebra, Master Math: Algebra, Master Math: Trigonometry, Master Math: Pre-Calculus and Geometry, and Master Math: Calculus are also fantastic!

5 comments about Introduction to Analysis.

1. This is an unusual and beautifully written introduction to real analysis. The presentation is carefully crafted and extremely lucid, with wonderfully creative examples and proofs, and a generous sprinkle of subtle humor. The layout of the pages is exceptionally attractive. The author has clearly put a great deal of thought and effort into producing an analysis text of the highest quality.

   Most of the book concentrates on real-valued functions of a single (real) variable. There is a gradual and careful development of the ideas, with helpful explanations of elementary matters that are often skipped in other books. For instance, prior to the chapter on limits of sequences, the book has a chapter on estimation and approximation, discussing algebraic laws governing inequalities, giving examples of how to use these laws, and developing techniques for bounding sequences and for approximating numbers. Proofs involving "epsilons" and "arbitrarily large n" make their first appearance here.

   The overall presentation of the book is carefully thought out. Each chapter is broken up into small sections, and each section emphasizes one principle idea or theorem. The proofs of the main theorems are lovely, and give both intuitive explanations and rigorous details. Genuinely interesting examples and problems illuminate the key ideas. Each chapter contains a mix of problems: "questions" that help students test their grasp of the main points of each section, "exercises" that are intermediate in scope, and more difficult "problems". (A solutions manual is available for instructors from the publisher.)

   The careful explanations, even of "elementary" matters, and two appendices on sets, numbers, logic, and methods of argumentation, make the book suitable for a first analysis course in which students have had no prior exposure to proofs. There is ample material for a one-semester, or in some cases a one-year, course.

   In summary, I believe that this is the best introductory real analysis book on the market. Students and instructors alike will find it a joy to read.




2. The book is slow to begin but it does a great job in explaining all the concepts. The author explains the proofs and theorems and it introduces some intermediate ideas to understand the theorems and definitions. The book contains a lot of exercise of different nature and difficulty. It covers a great range of subjects but not enough on the Rn. The book is basic in it contain, it is not difficult to read and follow. It can serve as an introduction to analysis. I would recommend it if you want an introduction to analysis.



3. I have always been hoping that there are more modern textbooks on the undergraduate math that are written by great mathematicians. This one is one of the first to appear on the market. Thanks for Professor Mattuck! I love you, and love your book more!!! Hehe....Oh, by the way, one day if you see a movie called A Wonderful Mind, then you'll find a guy featured in it whose name is Abel Maple. The future greatest mathematician of the 22 century. Just kidding!



4. I had trained as a physicist in college, and found this book useful when I began my PhD work in mathematics, where the way of thinking was just different enough to trip me up. My real analysis and Lebesgue integration class used the formidable classic "Introductory Real Analysis" by Kolmogorov and Fomin, and this book was a useful adjunct as I worked through the material for the class.
   
   The authors take a more explicitly numerical or equation-based approach to analysis than Kolmogorov and Fomin, who are more abstract and set-based. While this book does not go into topic Lebesgue integrals with anywhere near the depth of K&F, the appeal to numerical thinking is useful for helping someone in natural science get a handle on where the abstract math is going. When I read the authors' introduction, I was gratified to know that this book's approach stemmed from the travails that physics majors at MIT faced when they took real analysis!
   
   I found this book handy for the basics on the limits of sets and the Picard condition for ordinary differential equations. Its coverage of more advanced topics like Lebesgue integration is very light, but as an undergraduate text or as an adjunct for graduate students new to the field, it can be highly useful.



5. Mattuck's 400-page book (almost entirely single variable except for differentiation under the integral and double integrals up to one iterate being improper) does not deliver more topics and deeper results as books half its size. The second mean value theorem used for deeper results in Fourier series convergence and integral inversion is not covered as in books by Apostol and Stromberg. The Arzela-Ascoli and Wierstrass Thms are not covered as in the 150-page Goffman book. Limsup and liminf takes up only half a page. Instead the book is rambling and uses uncommon notations and definitions. Mattuck defines and uses widely the wavy equal sign in place of most statements on limits. The Riemann integral is defined differently then other books. The linearity of the integral takes two chapters to develop. Topology is not used in the significant way as in Stromberg, Rudin, and Rosenlicht to prove the intermediate value thm and the thm on the existence of max and min points in a compact domain using the preservation of connectedness and compactness by continuous maps. The book gets mired throughout in approximations and upper and lower bounds. Yet, the axioms of a complete ordered field (COF)is never stated even though Mattuck admits some good mathematicians trip over inequalities. Therefore, that all the fuss made in analysis is to show that the geometric and intuitive notions of calculus can be based on sets and the COF never comes through.

5 comments about Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review.

1. I have been using Korn and Korn for over 20 years, and have gone through two hardback editions, before buying the paperback one for my son who is studying electrical engineering. I would not have bought him anything else, because Korn^2 is the MOST complete mathematical reference book I have ever seen. It is infinitely more useable than Bronshtein and Semendyayev, and if you want to have one reference book Korn^2 should be your choice.



2. This Handbook has quite a lot of more formal math in it.
   
   Rade and Westergren's modern Handbook is more useful for finding the engineering equations you need, without all the formal stuff.
   
   I find both useful in different ways.



3. I have looked into a lot of mathematical handbooks but most are just junk. This one is the best available. The only one that is comparable to this is the one by Abramowitz and Stegun. If you need an applied mathematics handbook, go for this one.



4. This book is filled with formula's and theorems. However, one must have a basic understanding of all the formulas and theorems in order to understand most of them. If you love math and enjoy seeing how formulas and theorems are worked out this is an excellent book. Even though it is extremely thick. I had hoped they would explain in much more detail the order of operations. Other than that, it is a well put together reference book.



5. During 20 years of using the Handbook of Mathematics
   (by I.N. Bronshtein, K.A. Semendyayev)I was looking for an English written counterpart in this matter and sure enough I found it in this book. My point of view is personally based on engineering disciplines. With the help of Amazon's preview features it was a quick decision which book to buy. It has a well structured content, the concept is logically outlined, and discusses all chapters an engineer can ask for. That's probably why it has over one thousand pages, which makes it more a mathematical lexicon. The date of the publication might seem to be outdated, yet it proves that mathematic has become an almost static discipline engineers and scientists can rely on.

2 comments about More Joy of Mathematics: Exploring Mathematics All Around You.

1. If you enjoyed Pappas' "The Joy of Mathematics," then you should love this addition to the set. This book, like its predecessor, contains a diverse collection of concise, insightful discussions about mathematical topics and how they relate to the observed world. It develops ideas with an elegant simplicity by providing the reader with copious amounts of illustrations and diagrams. Pappas communicates mathematical ideas clearly and, unlike some mathematicians, stresses their relation to the lives and experiences of humans. She reveals the appealing aspects of the subject by excluding the technical, logical deductions that most frequently discourage people from studying it. The variety of topics presented in the book displays the versatility of mathematics and its relevance to human knowledge. For students interested in exploring the meaning and significance of mathematics or for teachers lacking the necessary materials to enlighten their students about these topics, this book is ideal.



2. Many have sadly been led to believe that math is a cold, lifeless subject limited only to homework assignments and balancing your checkbook. Nothing could be further from the truth, and Pappas books show this. Her "More Joy of Mathematics" shows a vast amount of instances of where math shows up, some math history, and a few visual brain teasers. How are exponents involved in the forging that creates a powerful Samuri sword? How do the properties of an elipse make your car's headlights switch to high-beam? What math can be found in an ocean wave, the strength of a honeycomb pattern, or a nautilus shell? How is math vital to the contruction of musical instruments? Is zero really a "number", and where does the concept come from? What are some currently unsolved problems in mathematics? A total layman could understand most of the book, but to understand all the mini essays you might at least want to have knowledge of math at the high school level.

   The book is a fast read, and fun to flip back and forth through, because each example is summarized in its own 1 or 2 page section, with illustrations. The same goes for "Joy of Mathematics" so you don't necessarily have to read that one first; they just contain different sets of examples. And don't think that all the good ideas were already taken for the first book -- "More Joy of Mathematics" is just as exciting to read. Plus it has a single index listing the topics from both this book and the previous one, so if you buy both it's easy to find the article you want by only looking it up once. Perfect gift for a math enthusiast at any level, and it may even covert a few "mathphobes".

No comments about Passport To Mathematics: An Integrated Approach Book 2.

5 comments about The Penguin Book of Curious and Interesting Numbers: Revised Edition (Penguin Press Science).

1. The various and quicksilver aspects of mathmatics is really where the charm lies for the scholar,as numbers themselves are the critters with which all scientific worlds are populated, the true scholar should begin with these first principles. A very good book for students who could use a few wows.



2. A great supplemental tool for teachers! I had terrific fun with my 6th grade math students when reading them certain passages in this book. Many of the topics covered, such as factorials, hexidecimals, triangular numbers, pi, primes, etc. are not generally covered in the middle school very well or at all, and this book serves as a great launching tool for discussions that kids enjoy and think about long after class is over. Also, many topics go in depth and will challenge even the best high school math students and take them in many directions that traditional math education does not.



3. In the foreword to G.H. Hardy's book A Mathematician's Apology, C.P. Snow tells an anecdote about Hardy and his collaborator Srinavasa Ramanujan. Hardy, perhaps the greatest number theorist of 20th century, took a taxi from London to the hospital at Putney where Ramanujan was dying of tuberculosis, Hardy noticed its number, 1729. Always inept about introducing a conversation, he entered the room where Ramanujan was lying in bed and, with scarcely a hello, blurted out his opinion about the taxi-cab number. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy! No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."

   Usually it takes a great deal of insight as well as considerable mathematical training to discover a yet unknown properties of some number. Only recognizing the beauty of a number pattern is much easier, though, especially with a friendly book like this one on hand. Wells, a long-time mathematics popularizer, has collected over 1000 numbers he considers interesting. Each of them is given a short explanation, often accompanied with a bibliographic reference. Celebrities among the numbers, like i, e or Pi, are given a more comprehensive treatment. Included are also several sequences, like Fibonacci's, Mersenne's, Fermat's, Carmichael's or Kaprekar's, each accompanied with its explanation. So are cyclic, amicable, untouchable or lucky numbers, and many more sequences you probably didn't know about.

   While Wells' dictionary certainly gives the impression of a well-researched work, the list of numbers is by no means exhaustive. Anyone familiar with chaos theory will notice the absence of Feigenbaum constant; prime hunters would probably be interested in discussion on Woodall primes, Sophie-Germain primes, or Proth primes. But they are better off with Paulo Ribenboim's book on primes, anyway, while Wells' book, with its easily understandable explanations and accessible price is probably more suited for the "recreational mathematics" audience.




4. Everyone has that smart-alex relation who ruins Thanksgiving dinner by proving to every four year old in the room that they know more about math than they do. There are several ways to deal with such a pain in the posterior but the least likely to involve violence and police intervention is this book.

   There are few `wonderful' books ... you can count them with the fingers of one hand ... this is one.

   The `smart-alex' in the family would call this book: `just a book on popular mathematics' thunder against it and not know 1/100 th of those facts within.

   This is understandable number theory ... I guess you could call it that. It takes a number, some whole integers and some fractional or decimal parts and tells you about them. What they are made off, how to use the number, how it was used historically ... in other words it not dry like those awful wiggly things scraggy armed Mr. Enngenheimer [whomever] bored you with in high school




5. does anyone even imagine that this little charmer pretends to be more than the wee delight that it is, and has been for decades? math, even recreational math, does expand over time; carpers can carp that this or that latest thing isn't here. but really, what IS here, page after page, will amuse and edify almost all readers.

2 comments about Math Dictionary: The Easy, Simple, Fun Guide to Help Math Phobics Become Math Lovers.

1. Math Dictionary: The Easy, Simple, Fun Guide To Help Math Phobics Become Math Lovers by Eula Ewing Monroe (teaches mathematics education at Brigham Young University) is a straightforward reference to basic mathematical terms for readers of all ages and backgrounds, from junior high and high school students to adults in need of a quick refresher. From "average" (including mean, median and mode) to "partial products algorithm" to "zero-dimensional" and much more, the terms cover general arithmetic, geometry, algebra, graphing, probability, statistics, and much more. Advanced mathematical terms such as those used in calculus are not covered. Each definition is spelled out in plain terms, often with simple diagrams to illustrate, eliminating any confusion. Amusing "Did You Know?" quips spice up Math Dictionary with amusing anecdotes such as how the number "googol" (ten to the hundredth power) got its name. Enthusiastically recommended for junior high and high school libraries.



2. If you spend any amount of time around me, and by that I mean about five minutes (sometimes less), you'll realize pretty quickly that I hate math. Hate it. Abhor it. Can't stand it. Oh, sure, I'm pretty positive that I use it occasionally, most of the time without even knowing it. But if you ask me a math-related question, I'm likely to give you a blank-eyed stare of confusion. Case in point: The other night my son, who will be ten years old in a matter of days, asked me the square root of 64. After the aforementioned blank-eyed stare of confusion, he proceeded to tell me that "square root" means a number that can be multiplied by itself to get the answer. Yes, there was more staring and more confusion. "Like the square root of sixteen is four, mom, because four times four is sixteen. And ten doesn't have a square root, because you can't multiply any number times itself to get ten." Oh, yeah, I knew that. Not.
   
   So when I received my copy of MATH DICTIONARY (whose additional title, by the way, is "The Easy, Simple, Fun Guide To Help Math Phobics Become Math Lovers") I was hit with feelings of both trepidation and wonder. Needless to say, I'm still not a math lover, but I think that with the help of this book, I can at least convince my son that I do, in fact, know the basics of mathematics.
   
   MATH DICTIONARY is an A to Z list of some of the most common terms you'll hear in a math classroom. Although the book doesn't cover advanced calculus or any of the hard-to-pronounce mathematical theories that the guy on the TV show Numb3rs likes to spout, it does cover basic mathematics, geometry, algebra, and even statistics and probability. It's all there, from abacus to longitude to zero property of multiplication--and everything in between.
   
   Although MATH DICTIONARY might not turn you into a math lover, it will keep you amused with its "Did You Know?" facts, which are actually quite interesting. It can be used as a handy reference guide to all school-age children, especially those delving into the harder mathematical arenas. And, for parents like myself who are outsmarted by fourth graders, it can definitely keep you from looking stupid. Or as un-stupid as parents can possibly appear to their children!
   
   Reviewed by: Jennifer Wardrip, aka "The Genius"

5 comments about Barron's Math Study Dictionary.

1. Helps to explain what a derivative and denominator is in terms that you and your children can understand. More than just the number on the bottom of a fraction.



2. We order these for our school teaching staff. The price is so reasonable that it costs under $500 to do this. That is less than the cost of a football uniform!!



3. This "dictionary" is really more than a book of word meanings. Explanations are detailed and well-written. The index and table of contents make it very easy to find exactly what you are looking for. I use this book in my math classes all the time. The information is grouped around similar topics. Well worth the purchase price.



4. I am studying to pass a teacher certification test for High School Math. Barron's Mathematics 129 page book is the perfect desk reference. It is a mini-encyclopedia of remarkable scope. Descriptions are short, informative, and interesting. Brief examples, diagrams and simple English explanations are precise and clear. Hundreds of fast math facts through pre-calculus. Don't throw out your math books that go into more depth but for quick lookups this book can't be beat.



5. i got this because i'm not very good at math and as my kids have progressed into junior and high school, i no longer understood what they were doing and am unable to help with their homework. i've tried to find a book that would take you step by step thru math problems. this book has helped some, but i can't find a book that clearly takes you thru the steps. also, it would be nice to have written rules, such as a clear and short explanation of how to do negative and positive numbers when multiplying, subtracting, etc.

5 comments about Q.E.D.: Beauty in Mathematical Proof (Wooden Books).

1. I like just about everything about this little book. There are a couple of other books on pictorial proofs out there (The Most Beautiful Mathematical Formulas by Salem et. al. and Proofs without Words by Nelson), but this one is by far the most visually appealing. I particularly like the beautiful etching-like illustrations which, in my opinion, capture the timeless beauty of the various proofs very well.
   
   Included in the book is a nice mix of well-known and not so well-known material. For example, many people will know the nifty pizza proof that relates the circumference of the circle with its area, but it is probably quite a pleasant surprise for many that a similar relationship exists between the surface of a sphere and its volume.
   
   B.t.w., and if you have also read the other reviews this may surprise you, I really did read most of the book.



2. Great little book! Mathematicians will often tell you that mathematics is beautiful. However, they usually have a hard time conveying the beauty of math to their nonmathematical friends. The author/illustrator has done a great job in capturing this beauty in the form of truly magnificent illustrations of proofs, making Q.E.D. the ideal read for anybody interested in discovering this elusive mathematical beauty for themselves.



3. I only submit this review in order to correct some of the other reviews. Apparently some folks don't accept that 1 = .9999...
   
   The proof is simple. Let x = .9999...
   
   Therefore, 10x = 9.9999... and x= .99999 and so, 10x - x = 9x. That is, 9.9999... - .9999... = 9.0000 (.9999... - .9999... = 0000...). That is, 9x = 9.0000. Hence, x = 1.000 since 9/9 = 1.
   
   Why does the mathematical operators allow the results to crank out 1 = .9999....? Because the "=" sign operates as an association of two different mathematical models in the sense 1 is a mathematical model for .9999... just as .9999... is a mathematical for 1. It was this thinking that led Descartes to assert y = mx + b whereby this equation constitutes a mathematical model of the line in algebra just as the line is a mathematical model of y = mx + b in geometry. All proofs involve mathematical models. Goedel numbers are models of theorems. See J. N. Crossley's little book or D'Abro's book on the rise of physics (volume one) for lucid explanations of mathematical modeling.



4. If you feel that you have lost the touch of history of mathematics, have lost your creativity into the rigour of formal methods, and need integral calculus to solve simplest of the mathematical problems, this is the book you need.
   
   Q.E.D. is a compilation of ancient mathematical problems with unexpectedly short mathematical proofs, which one you know them, are as simple as they can be, yet you may not think of them by yourself.
   
   My idea is to train (or re-train) my mind with that creative thought with which you can find elegant proofs to mathematical problems rather than resorting to differential equations at each point. This book is just great on that.
   
   I could work myself through half of the book in about two days. So thought-provoking is the content that I ended up proving a few theorems myself that were not included in the book. (Yet I see a simpler proof of one of them later in the book!)
   
   I wish this book included five times more material than what it has. I wish to have all of mathematics to be taught in this fashion. Had once encountered a problem from electromagnetism that I could not even start on, finally gave up and continued reading the Feynman lectures on Physics (vol 2) to see the proof. The proof, albeit more complicated than all proofs in this book, Q.E.D., was still unexpectedly simpler.
   
   I wish for a book like Q.E.D. that teaches me a lot more mathematics. But this is not to say that Q.E.D. hasn't served the purpose it aimed for.



5. Q. E. D. is an abbreviation for the Latin phrase "Quod erat demonstrandum", which means, "what had to be proved." In this book, Polster demonstrates 23 simple "proofs" of fundamental mathematical principles. I enclose the word proof in quotes because they are not always rigorous in the mathematical sense. In some cases they are more in the area of reasonably convincing reasoning.
   Some examples are:
   
   *) Cavalieri's principle
   *Archimedes' theorem
   *) The infinitude of primes
   *) The divergence of the harmonic series
   *) Slicing a cone by a plane will always give an ellipse
   *) Formulas for the sums of the first n-th powers.
   
   The mathematics is not rigorous, but that is not the intent here. The goal was to give a brief presentation and argument in favor of several fundamental mathematical principles. In my opinion, the author has found the mark, explaining these principles using language within the bounds of the merely interested rather than the learned professional.

5 comments about Actuaries' Survival Guide: How to Succeed in One of the Most Desirable Professions.

1. Contrary to the last reviewer, I found Fred Szabo to be a very good author. Starting with the structure of the book and ending with the chosen style, I rate it as an A plus written book. I strongly believe Fred Szabo to be very skillful in giving both a clear and concise presentation of new and complex material. Immediately from the table of contents one can follow the logical consequence of problems and questions a person would encounter if he or she wanted to become an actuary. Short and full answers can be easily found in this well organized text.
   
   Recently, actuarial jobs have become more and more popular. Good salaries, promising careers attract a lot of youngsters. Not to waste your time and dedicate yourself to a wrong career is very important in everybody's life. This book opens the door to what an actuarial career looks like, answers all standard questions, starting with typical responsibilities and ending with attainable salaries; it also guides the reader towards the right educational choice and explains what makes one a successful actuary. To spend time reading this book is a privileged shortcut to making the right career choice.



2. I have been searching with my students for a good book explaining challenges of the actuaries' job and the way to it. I could not find anything that would guide my students and help them in making an informed decision. Finally, I got Actuaries ' Survival Guide by Fred Szabo. I wish to share some of my thoughts with potential readers.
   
   The book should be considered as good guide for people who want to pursue their career as actuaries. It shows step by step challenges as well as opportunities of this job. Most of my students after reading this book were able to say if this is really the job they want or not. For all of them it was quite clear what are the demands and if they are able to fulfill them.
   Let me comment on the selection of topics. The content of the book is organized in a very logical way. It is as complete as it could be possible. We learn what is the actuarial job, what skills we need for it, types of accreditation, what education we must go through, how to start and continue an actuarial professional career.
   
   It would be important to mention the style of the book. At first sight it is very unusual. Large parts of the book are written in Q&A style. I have been thinking a while why Fred Szabo decided to choose just this style instead of something more conventional. Finally, I understood that this book written in traditional style of narration could be very difficult to read. Writing it in the form of questions and answers Fred is taking away this difficulty and forces his readers to concentrate on one topic at a time. There is another advantage to this approach. I guess, some of my students could never even think about problems that are mentioned in Fred's questions. For most of them reading these questions was quite a good lesson.
   Finally, we should look into answers. Who replied to these questions and how? It is evident that most of the answers were given by experienced actuaries. This book is not the knowledge of a single person; it is the wisdom of many top level professionals. As a scientist and author I admire the amount of work done in researching and writing this book. I admire the professionalism of Fred Szabo.
   
   In conclusion I would like to say that this is a wonderful book written in a professional way for the people who wish to be professionals in one of the most difficult professions.



3. As someone interested in making a possible career change into the actuarial profession, I purchased this book hoping to get a feel for the day-to-day job experience of an actuary, as well as get some basic information about career paths and professional organizations. A large portion of the book consists of responses a survey the author undertook; daily tasks, salaries, opportunities and such. These are very useful and are presented without "analysis" by the author, leaving the reader to draw their own conclusions. However, the book really has very little background information - differences (textbook at least) between different business areas actuaries are employed, or information about what distinquishes an associate from a fellow, etc.
   Upon further research I also discovered that some of the information has become out of date, as the professional organizations have recently added some additional requirements for advancement.
   Overall I did find this book of some use in understanding more about the "daily life" of an actuary, but with the lack of background info and some information becoming outdated I cannot recommend it at the $40 price tag it currently carries.



4. This is a compilation of mainly everything you can read at the CAS and SOA websites. It's a colletions for FAQs that actuaries in the industry answered and some of the questions weren't answered well. The second half of the book discusses the examinations which is a little helpful but again you can go to the websites for that. This book was not worth the price I paid.



5. Sorry to mislead. I haven't read the book, but having recently left the actuarial profession after 15 years, I can probably save you buying the book and tell you how to succeed in the profession:
   
   Pass Exams!
   
   No one cares about your personality, leadership skills, or anything else, when it comes down to it. It doesn't matter how good you are at your work related activities. In this profession, he/she who has the credentials is king/queen, and will get all opportunities for advancement. If you don't have the credentials, you can be the greatest business person and personality on earth, and you will not be recognized for it (not in this profession, anyway). I speak from 15 years experience. If you are getting in this profession, don't let anything get in the way of exam progress. You should know, to succeed, you should be willing to sacrifice possibly a decade of your life sitting in a dark corner studying advanced mathematics. I kid you not. I left the profession, because in my opinion, the payoff was not worth the sacrifice. That is, there are people making more money, that didn't have to go through the exam hell actuaries go through.