By Robert L. Causey - Logic, Sets, and Recursion: Mathematics Textbook (Revised Edition) [Paperback] - Perfect for University Students & Math Enthusiasts

The title of this book is VERY misleading, because although it does cover mathematical techniques in logic, it really is one of the few (if not the only in English!) introductions to what has today been lumped into "Discrete Mathematics," or colloquially "computer math or computer logic" that is appropriate for pre-undergrad, without linear algebra and calculus."Discrete" math is jokingly referred to in post grad math and IT teaching circles as "all the math they've taken out of the advanced High School curriculum, yet expect you to know as an undergrad freshman." If you're a REALLY advanced AP HS student, the powers that be grill you on inequalities, so you can place in the top percentile in math competitions!This is NOT a "symbolic logic" text as much as a pre- engineering/ computing/ math foundation for sets, recursion, induction, proofs and other foundation topics for advanced math, with a computational flavor. The 2001 edition is available (with 2003 revisions) CHEAP and has many of the best features of this extraordinary update if your goal is to self study review either professionally or pre-course. Some criticisms of the book ding the "lack of rigor," which is completely untrue! The book is logically, computationally and mathematically rigorous, but uses much simpler algebraic recursion notation in place of symbolic logic notation-- which you can easily pick up once you have the FOUNDATION of WHY recursion and induction are used for generalization. The criticisms are actually the very essence of the value of the text-- staying away from advanced notation and calculus/ linear algebra long enough to give you a GREAT foundation for both!This also is not, as some reviewers online have said, a "mathematical programming" book. Those reviewers are using the term incorrectly-- mathematical programming is a type of optimization (minimax) technique akin to "linear programming" (which, in itself isn't mainline linear algebra ala vectors/arrays, but also an optimization technique for "corner solutions" to mixing and other problems). The term they are looking for is "Mathematical techniques in logic" more usually generalized as the previously mentioned catch all bucket of discrete mathematics, which in reality (in postgrad) morphs into graph theory and dozens of other specialties.Causey covers all the "missing links" a new undergrad student needs before tackling ALL the advanced topics in math, engineering and computing. Perhaps unfairly, many of the finest engineering schools (I design engineering and computational complexity math tutorials for MIT, Harvard, Stanford, etc. and am a DSL Engineer in Robotics in my day job) USE these topics as a culling course to thin the herd. You've likely seen the pendulum from "new math" (set theory) back to SAT prep with TI and HP calculators, but "set theory" (which is now systems theory), when applied algebraically, becomes the foundations for numerical methods and other very advanced topics in all of math, computing and engineering. This is NOT lost on Causey, and every section is designed to prepare you, at a deeply intuitive and basic algebraic level, FOR the more advanced notation of symbolic logic and computational set - systems theories.The most amazing thing is that this is a proofs, not a techniques book! You'd think that would make it bland or nerve racking or galactically boring. NOT SO! If you're a community college, AP HS or beginning undergrad prof-- DO consider this fine text to prepare your young engineers for SUCCESS. If you're an auto didact, DO get this text to round out your foundation. I am VERY sensitive to budgets and am NOT happy with the price of this text, but frankly, as one of a kind, don't know what else to say other than consider used or the previous edition if you must! (BUT the 2005 2nd ed. has 112 more pages of exercises than the 2001 revised edition).Compared to a similar priced Springer text with half the pages, it is WAY more valuable for its intended audience as a one of a kind approach, and the 05 is over 500 pages compared to 400 for 01. But it's also a hidden gem, and we're right now trying to let our school libraries know about it just to help these programs, which will hopefully get the price down for you and make it more available in library systems. If your job is preparing math, computer science or engineering foundations, this is THE go to text. There are over 30 similar texts in Chinese that have not been translated that we've found so far in our literature reviews-- that says something!Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.