By Robert Jasiek, engl., 240 pages.
The book contains 40 major definitions and 149 statements of truth, of which 139 are proved in the book and 10 are taken from the literature. The statements of truth represent 60 theorems, 76 propositions, 11 corollaries and 2 algorithms. Besides, one lemma is embedded in a proof. Statements of truth are labelled as theorems, propositions or lemmas in decreasing order of relevance but mathematics does not use these terms consistently. The book refers to major results as theorems, intermediate results or preparations as propositions, and helping statements of truths as lemmas. Corollaries are derived by symmetry, trivial transformation, or as less general implications of theorems or propositions. For comparison, the book Mathematical Go Endgames about the microendgame and scoring has 24 statements of truth, of which 11 are theorems, 9 propositions (called lemmas), 1 corollary and 3 algorithms.
The average level of difficulty of the mathematics in this book is that of the first year of study at university. You can understand much with school algebra. The rich variety of proof techniques is a great source for learning them. Most definitions and theorems are understood easily like principles. The mathematical proofs are as detailed and step-by-step as is common at school. This is unlike mathematical books or journals read at university, where the student needs to think 30 minutes per line of text. The diligent reader has a chance to understand even the advanced proofs of this book by spending half an hour per page. A reader skipping the proofs misses half of the book's contents but can still learn a lot.
We study the fundamentals as well as advanced theory. We prove both the 'obvious' and the difficult. However, allegedly obvious theory may be easy or difficult, and has required between 20 minutes and three weeks per proof. Some proofs need one line applying theorem A to theorem B while the longest proof studies 30 cases on 11 pages.
A professional mathematician has proofread chapters 2 to 5
