European Mathematical Society - Oscar E. Fernandez
https://euro-math-soc.eu/author/oscar-e-fernandez
enThe Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love
https://euro-math-soc.eu/review/calculus-happiness-how-mathematical-approach-life-adds-health-wealth-and-love
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The subtitle explains more clearly what the book is about: <em>How a mathematical approach to life adds up to health, wealth, and love</em>. It is thus one of these books showing to the layperson how mathematics <em>can</em> be used in everyday life (not necessarily how it <em>is</em> used in practice). Therefore the mathematics are really elementary. Unlike similar books, written with the same purpose, here the health, wealth and love take up some serious part of the pages, and give only little mathematics in return.</p>
<p>
Let's start with the health. That subject has two chapters: one on the calories you take in and burn and one about the composition of your diet. What you get to digest for mathematics is a weighted linear sum of components such as your age, weight, and height that are influencing your metabolic rate, your calorie burning, or your cholesterol ratio. A simple quadratic defines your maximal heart rate as a function of age, and the expected years of life loss as a function of waist to height ratio.</p>
<p>
The second part has the promising title <em>A mathematician's guide to manage your money</em>. This also has two chapters. One is about managing your budget and the second about financial transactions like saving and investing. The mathematics we learn here is that taxes are computed in a linear way but only within certain intervals, so that it is actually a piecewise linear function. Also we learn what a compound interest rate is (or inflation rate in this case) and this leads to Euler's constant e and consequently also to the logarithm. A glimpse at the financial markets is the occasion to introduce some statistical concepts like average and standard deviation.</p>
<p>
The 'love' part introduces a formula to compute the number of possible dating candidates, and the well known 37 percent rule which states that if you need to select the best one (for example partner among the candidates) in a sequence, then you should first register the best candidate among the first 37% of the sequence and then take the first one that is better than that one. It also describes the Gale-Shapley algorithm to solve the stable matching problem. The last chapter is mathematically the most involved one of the book and analyses the relation between two persons as a dynamical system described by two simple differential equations. Also the Nash bargaining problem is discussed in which the optimalization of the quadratic Nash product has to be found when the couple has to come to a joint decision.</p>
<p>
Most of the mathematical derivations and computations are removed from the text and are summarized in appendices and if you want to apply it to your own life, you don't even need a pocket calculator because the publisher's web page has a link to online apps that will evaluate the formulas for you when you introduce your data. Each chapter also ends with a summary of the mathematical and nonmathematical takeaways. If you are interested in one of the topics, further reading is provided. Indeed, all the equations and methods described here are abstractions and usually drastic simplifications of reality. Therefore I would also like to refer to a don't-try-this-at-home type of warning that Fernandez provides in the introduction: if you want to implement major changes in your life based on the methods presented in this book, be sure there is an expert (like for example your medical doctor) to assist you and give good advise.</p>
<p>
I doubt that the noble hope of the author, which is that by reading this book the reader will adopt a mathematical approach to life, shall be fulfilled. The mathematics are really precalculus, while the problems like composing a diet, financial investment, and finding a partner for life, do not seem like the problems one is facing at the age one is brought in contact with the required precalculus. Somehow I think that the level of the applications and the level of the mathematics do not match well. There are however still wise lessons to learn from the book which anybody (certainly journalists and politicians) should know. For example one should have the numeracy to know that doubling the price of a sandwich over 10 years, does not mean that the inflation is 10% per year. Also the mathematical techniques shown here do not only apply to the three main topics enumerated above, but they are also applicable in many other situations, like an optimal selection of a secretary or the best way to subdivide a pizza among a number of hungry children.</p>
<p>
I believe it would take a student already interested in mathematics to be sincerely attracted to reading the book. On the other hand, teachers may find inspiration in some of the examples to use these as illustrations in their teaching. Or perhaps the mathematics that are used in the book may be an inspiration for them to apply it in perhaps similar applications that are more adapted to their particular set of students.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is another book showing the use of mathematics in everyday life. The mathematics are rather elementary and include simple functions like linear, quadratic, or cubic at most (in relation with calorie consumption, or composing a diet), the computation of interest or inflation and the logarithm as well as mean and standard deviation (in connection with managing a budget or investment) and the 37% rule for making an optimal selection in a sequence, an algorithm for the stable matching problem and the Nash bargaining problem (to solve partnership and relational problems).</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/oscar-e-fernandez" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Oscar E. Fernandez</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691168630 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">19.95 £ (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">176</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10952.html" title="Link to web page">http://press.princeton.edu/titles/10952.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li></ul></span>Thu, 20 Apr 2017 13:35:20 +0000Adhemar Bultheel47635 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/calculus-happiness-how-mathematical-approach-life-adds-health-wealth-and-love#commentsEveryday Calculus: Discovering the hidden math all around us
https://euro-math-soc.eu/review/everyday-calculus-discovering-hidden-math-all-around-us
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
As a mathematician, it will not be difficult to connect mathematics to everything you see around you. Look at a tree and you may think about complex fluid dynamical modeling problems for the lifestream pumped from the roots to the leaves. If you look out of the window, you may associate it with the control problem at the factory to produce flawless glass panes.</p>
<p>
Fernandez does something similar, although at a much less advanced level of mathematical complication. In fact he follows the backbone of an elementary calculus course: functions, limits, continuity, derivatives, curvature, (simple) differential equations (mathematical models), optimization, integrals and their applications. As he walks through the calculus course, he describes in parallel an ordinary day in his life and with every event or moment he can associate a mathematical issue. The level of the mathematics is elementary, although sometimes he lifts it to a somewhat higher level. So I am not sure what kind of public will appreciate this book most. If as a reader I am a true mathematical virgin, then it is nice to see how changes in stock markets can be used to evenually lead to the definition of a derivative, but if I am interested in stock markets, I will probably not be a mathematical virgin. If on the other hand I do know my calculus course, then I would probably be a bit bored by the time it takes to finally arrive at the derivative which I already know. So I guess that the readership that will appreciate this most will probably be the people who did have a calculus course long ago, but who have forgotten most of it, and never understood why they had to spend so many hours of their youth studying mathematics, that they never needed or made use of afterwards.</p>
<p>
It takes not a lot of imagination to link almost any application you have in mind to almost any instant of and average day of your life. If there is nothing triggering the application in a visual of auditive way, it suffices to say that looking as X, it makes you think of Y, and there you are. So the fact that Fernandez is describing an average day in his life is not very important, it's just a backbone on which to hinge the successive chapters, which happen to be the successive chapters in a calculus course. The originality is just the applications chosen to illustrate the mathematics.</p>
<p>
Let me take the first chapter as an example. When waking up, a discussion is given about the periodic REM sleep as a sinusoidal phenomenon. The alarm can be an alarm clock working on AC current or an iPhone working on DC current. That triggers a rather elaborative discussion on electricity and why AC has defeated DC when it comes to transporting electricity over longer distances. Think further of radio waves and audio waves decaying at a logarithmic rate, and think of the parabolic path of the jet of water from the shower under influence of gravitation and clearly there you have enough examples to introduce the elementary functions: trigonometric, logarithmic, polynomials,... The other chapters are similar, gradually increasing the mathematical level. Chapter two is breakfast, listening to increase/decrease on stock market products is about changes, i.e., derivatives. Similarly the cooling down of the coffee, or the deterioration of the effect of vitamin pills is about the derivative shaping the decay. Other (traditional) examples are the speed of a raindrop under gravity with air resistance, the change of unemployment rate,... An example that one would not expect in an elementary calculus course is the correction needed for a GPS signal because of Einstein's relativity theory. Since the GPS signal travels at the speed of light, relativity requires a correction to calculate the spatial position, otherwise it would introduce an error of about 1.34 miles per day (all quantities are expressed in American units, no standard metric system in this book). Some other topics discussed: spam mails reducing productivity, the chance of catching a cold from somebody, the sustainable amount of fish to catch, the optimal angle at which our blood vessels are branching, the optimal pricing of a theater ticket, traffic speed control over a road section. The introduction of Riemann sums and the integral is kept rather mathematical until it comes to the applications: a thermostat, an optimal seat in the movie theater, the length of a train track, the expanding universe. A nice feature of having different applications is that Fernandez shows that the same mathematics and even the same formulas will provide answers to problems that seem to be totally unrelated at first sight.</p>
<p>
Some details about steps made in the main text are further elaborated in appendices. There is a confusing typo on page 55 where it says that some graph is curving upward (convex) and later curving downward (concave). This curvature is expressed by the second derivative (first positive, later negative), but it is given the wrong sign in the book.</p>
<p>
To conclude we can say that the author is trying very hard to show that mathematics is all around us. In that respect he certainly succeeded. It's a laudable achievement that he brings this with illustrations that are both modern, nontrivial, even including relativity theory and cosmology. As a mathematician he is emphasizing the fun of realizing that the math is really able to model and solve these (simplified) problems. As a mathematician one may easily understand these feelings and enjoy it as much as Fernandez does. However, when reading this with the eyes and mind of a youngster, who feels annoyed and bored with all these mathematics, and who does not care about all the mathematics governing whatever he is doing, which he will do anyway, whether or not he understands the underlying mathematics, I am not sure that such a student will experience the same 'fun' as the author experiences. What I am missing a bit is the playful element that generates the true 'fun' for the not-yet-mathematician, and a bit of the challenge that is needed to really engage the reader. I do not think the book will convince the non-believers, who couldn't care less about all these mathematics. They will not be convinced because the mathematics are too explicit and hence for them the book will be a bit less boring than their lecture notes, but probably still boring. On the other hand, the book is perfect for a reader who really wants to know what mathematics are governing our lives and who wants to learn and understand or polish up his rusty knowledge of these mathematics.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Fernandez illustrates a basic calculus course from functions over limits, derivatines up to integrals by taking examples from an average day he spends from waking up and having breakfast to going to sleep after having diner and watching a movie. It is not difficult to link every instant in the day with a topic from the calculus course. Some excursions are surprising like the branching of blood vessels, time travel and relativity and cosmology. Basic definitions and elements of the mathematics are included and sometimes further elaborated in appendices.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/oscar-e-fernandez" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Oscar E. Fernandez</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2014</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0691-1-5755-9 (hbk) </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£16.95 (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">168</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://press.princeton.edu/titles/10199.html" title="Link to web page">http://press.princeton.edu/titles/10199.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a05</a></li></ul></span>Mon, 12 May 2014 18:30:02 +0000Adhemar Bultheel45562 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/everyday-calculus-discovering-hidden-math-all-around-us#comments