Thinking Better: The Art of the Shortcut in Math and Life by Marcus Du Sautoy
Math relies on building blocks and shortcuts to help quickly get to conclusions. Multiplication is a fast way of doing repeated addition. Exponents are just repeated multiplication and good by done by repeating additional over and over. However, shortcuts enable doing these in simpler fashion. More advanced math like calculus are essentially just shortcuts to solve certain types of problems. There are many shortcuts that can be found in math. Spotting patterns and shortcuts can help quickly resolve problems. Likewise, in life there are many shortcuts that can be found to quickly come to an accurate conclusion. However, like math, there are also some things that require doing things the "hard way", like practicing an instrument.
Big data has the potential to erase past prejudices and provide an equal playing field for everybody. Rather than rely on biased feelings, computers can look just at the numbers to make objective decisions. This could allow previously redlined groups better access to loans and money. It could help with hiring and termination of employees. It could also better target resources to improve education and reduce crime. Big data could also help companies make a lot of money.
Statistics can be powerful, but also mystical. This book attempts to take the mystery out by building up knowledge from the ground up. Statistical topics are developed using real world applications and then analyzed from a "brute force" method. Then the math is applied as an "easy solution" to the problems. The author also pull from his experience using statistics in various cases. One that is covered multiple times is the doctor that had killed is patients. Naive statistical analysis could have caught him. However, it would also have caught innocent doctors. It is important to do more thorough statistical analysis as well as look at the real world conditions. The book concludes with an analysis of statistics and the state of scientific research. P-values have been taken as gospel and many "tricks" have been used by researchers to get publishable results, even if these are not really meaningful.
Statistics can be a source of much confusion. I recent newspaper article stated "only [small number]% of coaches are women, yet [large number] girls play this sport." The goal was to saw there is a great shortage of female coaches. But using a percentage in one place and number in another is misleading. "Just 5% of coaches are female, while 5,000,000 girls play this sport" sounds really bad. But if there are also 500,000,000 boys that play the sport, it actually shows female coaches are over-represented. Numbers and statistics are a great way to tell these "lies".
A Tour of the Calculus attempts to explore Calculus from a practical, evolutionary point of view. What can we do with it? What is useful. There are many conversational pieces as the author "talks" with some of the key contributors to modern math and learns what they have done and why. It tries to be conversational, but does resort to a bit of mathematical notation. It almost worked for me. While I did get many key insights into Calculus, I found it got just a bit too much into the details to keep me from being able to focus on the general narrative. 
Humble Pi is a fun book about math gone bad. Or perhaps smore accurately, it is about humans' poor understanding of numbers. There are big disasters and little flubs described. Bridges collapsed because minor changes greatly increased loads. McDonald's went to court because they seemingly exaggerated the number of meal combinations. Other companies understated the number of combinations. People have been given lethal doses of medications due to misunderstandings of the unit of measurements. The Gimli Glider was a 767 airplane that ran out of fuel midflight. Luckily, the pilot was able to glide it down to a landing. A number of things together created the issue. However, a key issue was the use of wrong units for fuel calculations.
The traveling salesman problem is a popular computation problem that has evaded a simple solution. The goal is to travel from one point through a number of different points just once and eventually return to the starting point. There are practical applications in route planning as well as many other areas. However, the solution has evaded a simple solution. The brute force solution grows exponentially as more points are added. Some heuristics can be used to help get a "good" solution and then iterate on it until it becomes optimal.
I think I liked the original title, Dots and Lines, better. However, Introduction to Graph Theory was what I was searching for. This book is getting close to 50 years old. However, the basics of graph theory still remain. Perhaps the only part that caught me off guard was the mention that the 4-color problem had not been proved. Alas, when I got to the end, the author corrected this with mention of the proof. (It came out right around the time this book was published.) 
The Fascinating World of Graph Theory is an introduction to graph theory that focuses on the interesting puzzles and participants in historical context. It introduces core concepts in graph theory as they are needed to tell the story. In doing so, it also provides the biographical history of the mathematicians that were involved in identifying and solving the problems. It is not quite an "introduction" to graph theory, though it does cover basic concepts. A deep math background is not required to start the book. However, the mathematical details and proof due appear. They can be understood in the context of the book (though I did have to occasionally go back to recall what a certain symbol meant.) I did enjoy reading the brief histories of the problems. These were interspersed with the math. There are plenty of problems that could help this be a "math textbook", while there is also historical information for a "general history of science". However, it doesn't quite fit into either category and instead rests somewhere in between.
The Joy of x attempts to demystify math so that "the rest of us" can gain some of the excitement that mathematicians do. The author succeeds fairly well in relating complex mathematics to the real world.
Despite the title, the Math Myth is actually pro math. However, it enunciates many concerns with the way that math is taught and used as a "weed out". Most students are required to take standard math classes. These classes are often taught by adjunct professors, because the full professor do not want to teach them. This leaves most students exposed to mediocre math instruction and has also led to a decline in those studying math. The courses have also "weeded out" many students who would otherwise be able to complete degrees.
Infinite Powers explores the evolution of calculus and the important roll that it plays in our lives. Both the concepts of "0" and "infinity" are key to the understanding of the world. However, these were not universally understood concepts in the ancient world. Many mathematicians did understand bits of it, but it wasn't until Newton and Leibniz separately put it all together. 
How Not To Be Wrong is part an exploration of the joys of math, and part a manual on how to avoid getting duped (or duping oneself) with math. There is also a bit of namedropping of famous mathematicians for good measure. Politicians are great at coming up with good sounding, but meaningless numbers. Wisconsin may have claimed that its 5000 net new jobs accounted for 50% of all new jobs for a year. That could be technically correct. However, since some states lost jobs, a state with 12000 net new jobs would claim to account for 120% of net new jobs, showing the craziness of the data. Science is also rife with "statistically significant random results" from insufficiently large or small studies. There is also a "survivors bias", with many failed studies not being published. If 20 people study something, one is likely to randomly discover a significant result. If that person is the only one to publish, we don't realize the significant result was just random. The "5%" p-value acceptance threshold is just an arbitrary value. However, it does result in a serious amount of 'p-hacking' There are a lot more studies that just meet the threshold than would be suspected by a normal distribution. Similarly, people tend to favor numbers ending in 7 as "random numbers". Thus, an excessive preponderance of vote counts ending in 7, may indicate a rigged election.
In Zero, Math journalist Charles Seife explores the concept of "0" and at the end brings in zero's cousin, infinity. Many ancient cultures did not have the concept of zero. The led to numerical systems like Roman numerals. It also resulted in odd year number. (1BC is followed immediately by 1 AD). Zero helped unlock new abilities in math, and made writing numbers easier. The author also explores Pythagoreans and their problems with irrational numbers (such as the square root of 2 that pops up in the pythagorean therom.) He mentions incidents where division by zero caused great calamities. Zero also opened the door the calculus and the concept of limits that approach zero (or infinity) Towards the end, the author spends a lot of time delving into worm holes and theoretical physics.
Fooled By Randomness explores the importance of random events in life and society. On the outset, the author states that he wanted this book to be fun to write, and tried to avoid too many citations. He does cite some literature, but more often he helps provide alternate explanations for results. For example, many studies have tried to tease out what makes successful businessmen. Intelligence is not seen as super important. However, the propensity to take risks does stand out. However, if you looked at bankrupt businessmen, you may see similar results, likely with an even higher "risk taker" rating. The highly successful may appear to be average because they are. They just happened to get lucky. The finance world tends to revere the young, successful traders. However, finding the next "big shot" is essentially a crap-shoot. One person may take risks and get lucky. However, many others will not have the same luck. An older trader is probably your best bet, because they have managed to survive for a long time without imploding.
Bayes' rule seems very simple. However, it has produced a great deal of controversy throughout its history. Even the name itself is controversial. Bayes does appear to have been one of the first people to produce a paper on it. However, the paper we have was substantially edited by Richard Price and presented at the Royal Society after Bayes' death. Laplace later independently discovered the algorithm and ran with it. Since he was the more renowned mathematical mind, it would make sense to name it after him. However, it was later referred to as Bayes rule by those who popularized it, and that is what we have today.