A how-to book filled with step-by-step instructions as to how the mathemagician Arthur Benjamin — being both a mathematician and a professional magician himself — manages to pull off gigantic calculation off of top of the head. Highly stimulating and practical.
An all-time cl
assic in mathematical initiation written in quasi-literary style by two prominent 20th-century mathematicians. It encourages problem solving as a means of developing new insight and genuine comprehension in higher mathematics.
The culmination of decades of teaching by one of the world's most prolific educator in linear algebra. In ~500 pages. It features conversational-style narratives coupled with review sections and challenge problems, while maintaining a focus on geometric intuition and real-life applications.
Accessible, ultra-comprehensive textbook on almost everything calculus has to offer. 30 years in the making and focuses on conceptual understanding while balancing the need for readability and rigor. Each section comes with a motivating discussion, followed by several solved examples and tons of problem sets afterwards.
A solid textbook on probability and statistics from the mathematical standpoint. It requires calculus and strikes a fine balance between applications and rigor.
A unique, 170-page book with a systematic approach in identifying, categorizing and explaining a mathematical proof and its making. Written in conversational style with clarity and accessibility in mind. Also featured are 15 video lectures and solution manual on the book's website.
A 300-page classic which takes a reader from not knowing what a proof is, to being able to carry out a proof proficiently. Notable features include conversational-style instructions, extensive proof illustrations and gently-crafted exercise sets. Highly accessible and does not require more than high-school algebra.
A solid, accessible, 400-page textbook on first-year abstract algebra. Clearly formatted with straight-to-the-point presentation and a surprising amount of examples both within and after a section. Ideal for both self-study and reference purpose.
A unique 250-page textbook covering the material of a second course in linear algebra through a non-standard route (i.e., without resorting to the concept of determinant — which is nevertheless introduced in the last chapter of the book). The 3rd edition represents a major improvement both in terms of formatting and exercise set expansion.
A 800-page survey as to what discrete mathematics has to offer. It's written in clear, accessible prose and include tons of solved examples and exercise sets.
A de-facto bible in discrete mathematics. Accessible, application-driven and rich in visuals and problem sets.
A solid-yet-accessible textbook which presents an unifying view of first-year real analysis, where each section starts with some historical motivation and contains many engaging examples and the thought process through which an analysis problem can be solved.
A 400-page review guide covering 1370+ solved and unsolved problems in anything advanced calculus. Particularly useful for people in need of boosting their advanced calculus skill in a short amount of time.
A clearly-written textbook which demystifies complex analysis through a series of accessible discussions, solved examples and problem sets. Ideal for students in engineering and other applied sciences.
A clearly-written, well-o
rganized textbook on numerical analysis which strikes a fine balance bet ween rigor and applicability. It features clear expositions, solved examples and relevant MATLAB codes all throughout the text.
A comprehensive, mostly-non-technical survey on how critical thinking and different forms of logic plays out in our daily routine, with Part II of the book dedicated to the development of formal logic and other math-based reasoning.
A comprehensive, accessible textbook on first-order logic and its associated meta-theory. It's based on the proof system Fitch and covers logic at both introductory and intermediate levels for students majoring in philosophy.
A standalone, 500-page textbook in introductory geometry written by a former winnder of USA Mathematical Olympiad. It features concise explanations along with 900+ problems from trivial to very challenging. Useful for developing one's geometric intuition and spatial reasoning skill.
A standalone, 300-page guide that teaches introductory LaTeX through countless examples. It strikes a fine balance between breadth and depth and ensures that by the end of the book, a reader will be able to produce a professionally-typesetted document on their own.
An up-to-date, standalone 500-page LaTeX manual that goes into the nuts and bolts of mathematical typesetting. Two decades in the making and contains a ton of examples (e.g., code vs. its output) and the do-and-don't.