
Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His mathematical work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in philosophy, linguistics and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon-vivant and a womanizer, who played the 'great man' to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism, but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of war saved his life and turned his career around, even while it separated him from his family for years. By the war's end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full length biography places Tarski in the social, intellectual and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man, interlaced with an account of his major scientific achievements.
I highly recommend the following two books to study Logic from the beginning (for a layman);
Logic: An Introduction to Elementary Logic by Wilfrid Hodges.
Introduction to Logic: and to the Methodology of Deductive Sciences by Alfred Tarski.
Also i highly recommend everybody to read the great logician Alfred Tarski's classic book Introduction to Logic: And to the Methodology of Deductive Sciences to really understand "Logic" which is what Formal Reasoning is based on.
Instead, what is taught is starting with truth tables for logical operators and thus students simply don't learn to think/understand. For example, almost everybody is thrown off by the "implication" logical operator (evaluates to True when the antecedent is False irrespective of the consequent). But if you use some actual domain examples then it becomes clear why it is so.
Alfred Tarski's classic book mentioned above does a good job of building up logic from the first principles and hence is a great companion to any standard textbook.
Some of the resources are so good that they bend your mind completely in a good way and you find out new avenues of thought and learning. You fall in love with a subject and pursue further.
I have two favourite courses for programming:
1. How to Code 1 and 2 by Gregor Kiczales on edX. They are based on the book How to Design Programs
2. Brown University's Acclerated Intro to CS course by one of the authors of HtDP: CS19. You can find it here: https://learnaifromscratch.github.io/software.
I have two favorite math books that have helped me understand more math:
1. Introduction to Logic by Alfred Tarski
2. Vector Calculus by Hubbard and Hubbard
What are yours?
I spend a lot of time thinking about philosophical-ish stuff, so here are some books that have had the strongest residual effects (whether that's changing how I think, changing what I think about, changing my values, or simply getting the thought ball rolling faster):
Ishmael (Daniel Quinn)
1984 (George Orwell)
Brave New World (Aldous Huxley)
Godel, Escher, Bach (Douglas Hofstadter)
The Republic [imp. "the allegory of the cave"] (Plato)
The Genealogy of Morals (Friedrich Nietzsche)
The Social Construction of Reality (Peter L. Berger, Thomas Luckmann)
Tractatus Logico-Philosophicus (L. Wittgenstein)
Dissemination [imp. "The Pharmakon"] (Jacques Derrida)
The Quest for Reality (Barry Stroud)
Languages of Art (Nelson Goodman)
The Structure of Scientific Revolutions (Thomas Kuhn)
Concepts (Jerry Fodor)
The Web of Life (Fritjof Capra)
Foucault's Pendulum (Umberto Eco)
Naming and Necessity (Saul Kripke)
Zen and the Art of Motorcycle Maintenance (Robert Pirsig)
There are others, and a lot of essays (by thinkers like Bertrand Russell, Carl Hempel, Hilary Putnam, WVO Quine, Karl Popper, Alfred Tarski, Gottlob Frege, David Chalmers, Daniel Dennett, Michel Foucault, Jean Baudrillard, Mikhail Bakunin, CS Peirce, and David Hume, among many others), but these seem apropos as they most readily came to mind.