Logical Methods
Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging.
This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more.
In the book you will, among other things, find answers to:
- What is a proof? What is a counterexample?
- What does it mean to say that something follows logically from a set of premises?
- What does it mean to abstract over something?
- How can knowledge and information be represented and used in calculations?
- What is the connection between Morse code and Fibonacci numbers?
- Why could it take billions of years to solve Hanoi's Tower?
Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.
Buy the book from Springer or Amazon, or read more about the book on Roger's home page.
The courses
Logical Methods is used as a textbook and resource several places!
- IN1150 - Logical Methods for Computer Science at Department of Informatics, University of Oslo, is using Logical Methods as the main book. This course is given every spring and fall (as an online course in the fall), and it is an obligatory course for many of the Bachelor students at the Department of Informatics.
- TMA4140 - Discrete Mathematics at the Department of Mathematics, NTNU, is using Logical Methods as the main book (with the additition of some number theory and cryptography). This course is given every fall.
Errata
The following is an overview of all known typos and errors in the book. If you find any errors that are not stated here, send an email to rantonse@ifi.uio.no and let me know.
- marks minor errors without significant impact on the content (typos, spelling mistakes, etc.)
- marks things that can be improved, but are not strictly incorrect
- marks inaccuracies, corrections, and mathematical errors
Last updated: 2023-02-03
Errata for the first edition (2021)
- s. 7, definition 1.1, last sentence: “A set can be specified by writing the elements between the symbols { }” → “A set can be specified by writing the elements, with commas between each element, between the symbols { }” (LAH)
- s. 9, last sentence before the digression: “an empty bottle empty is not empty” → “an empty bottle is not empty“ (NEH)
- s. 95, line 2–3 from below: the phrase «with a proof by contradiction» should be removed, because this is a direct proof that a statement is not true (LT)
- s. 119, exercise 9.13 (i): «{3,4,5,8,9,12,16,17,20,24,33,...}» → «{3,4,5,8,9,12,16,17,20,24,28,32,33,...}» (RA)
- p. 149, middle of the page: “Between two” → “Between any two” (RA)
- p. 155, the example, line 3: “Pa P is true for a” → “Pa ∧ Px P is true for a og x” (RA)
- s. 165, exercise 14.4 (h): «∀x∀y(y+x→x+y)» → «∀x∀y(y+x=x+y)» (VNK)
- p. 168, the definition, line 2: “a function” → “a function ·M (written as a superscript)” (RA)
- p. 174, second solution: Remove the parenthesis around the arguments of P and Q. (RA)
- p. 187, the digression, line 3 from below: “this” → “(8)” (RA)
- p. 187, line 5 from below: “the first case” → “the second case” (RA)
- p. 216, the digression, line 7 from below: “1939” → “1938” (RA)