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.

- Addition
- Substraction
- Multiplication
- Divis
**ion

- Memorizing large numbers
- Calendar-related calculation
- Guess-estimation
- Vedic division

An all-time classic 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.

- Elementary number theory
- Analtytic geometry

- Topology
- Calculus

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 section**s and **challenge problems**, while maintaining a focus on **geometric intuition** and **real-life applications**.

- Matrices
- System of linear equations
- Vector space
- Orthogonality

- Determinant
- Eigenvector
- Singular value decomposition
- Linear transformation

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.

- Derivatives
- Derivative applications
- Integration Techniques

- Partial derivatives
- Multiple integrals
- Lagrange multipliers

- Divergence / Curl
- Applications of integrals
- Differential equations

A solid textbook on probability and statistics from the mathematical standpoint. It requires calculus and strikes a fine balance between applications and rigor.

- Probability distributions
- Moment-generating functions
- Law of large numbers
- Central Limit Theorem

- Methods of estimation
- Analysis of variance
- Non-parametric statistics
- Bayesian inference

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.

- Forward-Backward Method
- Construction Method
- Choose Method

- Generalization
- Unification
- Dual Representation
- Abstraction

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.

- Basic logic
- Elementary set theory
- Proof techniques
- Mathematical induction

- Relation
- Function
- Infinite set
- Schröder–Bernstein theorem

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.

- Set
- Integer
- Group
- Ring

- Integral domain
- Field
- Complex number
- Polynomial

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.

- Vector space
- Basis
- Linear mapping
- Polynomial

- Eigenspace
- Inner product space
- Duality
- Spectral Theorem

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**.

- Set Theory
- Logic
- Proof techniques
- Relation

- Sequence
- Recurrence relations
- Cardinality
- Counting techniques

- Graphs
- Logic circuits
- Algorithmic efficiency
- Finite-state automata

A de-facto bible in discrete mathematics. Accessible, application-driven and rich in visuals and problem sets.

- Set / Logic
- Function
- Algorithmic complexity
- Cryptography
- Recursive structure

- Spanning tree
- Boolean algebra
- Logic circuit
- Turing machine
- Structural induction

- Cardinality
- Modular arithmetic
- Recurrent relation
- Generating function
- Counting techniques

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.

- Limit
- Sequences
- Series
- Point-set topology

- Continuity
- Derivatives
- Uniform convergence
- Integrals

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.

- Sequence
- Series
____ - Derivatives
- Integrals

- Partial derivatives
- Multiple integrals
- Fourier series
- Complex variables

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.

- Complex transcendental functions
- Analyticity
- Contour integration
- Cauchy integral formula

- Laurent series
- Residue mapping
- Conformal mapping

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.

- Numerical root-finding
- Interpolation
- System of equations
- Least-square methods

- Numerical differentiation
- Numerical integration
- Numerical ODE methods
- Numerical PDE methods

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**.

- Propositional logic
- Predicate logic
- Natural deduction
- Rules of inference

- Inductive reasoning
- Legal reasoning
- Probabilistic reasoning
- Statistical 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.

- Translation
- Turth tables
- Fitch

- Axiomatic set theory
- Mathematical induction
- Löwenheim-Skolem Theorem

- Compactness theorem
- Gödel's Incompleteness Theorems

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.

- Angle
- Similar/congruent triangles
- Quadrilaterals
- Power of a point

- Polygons
- Circles
- 3D geometry
- Transformation

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.

- Installing LaTeX distribution
- Formatting text
- Designing page layout

- Customizing lists
- Float environments
- Cross-reference

- Typesetting math
- Adjusting font
- Hyperlink

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.

- Symbols
- Preamble
- Font
- Spacing

- Page layout
- Math expressions
- Proclamation
- Proof

- Beamer
- Tikz
- Bibliography
- Index