- Paul S.
**Addison**: Fractals and Chaos*****

An Illustrated Course - Martin
**Aigner**, Günter M.**Ziegler**: Proofs from THE BOOK******

- mathematical results that are beautiful, accessible, and profound - Martin
**Aigner**: A Course in Enumeration*****

- the power of combinatorics - Avner
**Ash**, Robert**Gross**: Elliptic Tales

Curves, Counting, and Number Theory - Avner
**Ash**, Robert**Gross**: Fearless Symmetry

Exposing the Hidden Patterns of Numbers - Michael F.
**Barnsley**: Fractals Everywhere*****

- the power of iterated function systems - Craig
**Barton**: How I Wish I'd Taught Maths

Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes - Martin
**Baxter**, Andrew**Rennie**: Financial Calculus

An Introduction to Derivative Pricing - Marcel
**Berger**: Geometry Revealed******

A Jacob's Ladder to Modern Higher Geometry - Rey
**Casse**: Projective Geometry: An Introduction

- a formal, coordinate-based approach - Fan
**Chung**, Ron**Graham**: Erdös on Graphs

His Legacy of Unsolved Problems - William S.
**Cleveland**: The Elements of Graphing Data

- effective graphical presentation of data - John H.
**Conway**, et al.: The Symmetries of Things******

- repeating patterns, from the plane to higher dimensions - H.S.M.
**Coxeter**: Projective Geometry

- an elementary approach emphasizing geometric intuition - Florin
**Diacu**, Philip**Holmes**: Celestial Encounters

The Origins of Chaos and Stability - Apostolos
**Doxiadis**, Barry**Mazur**: Circles Disturbed

The Interplay of Mathematics and Narrative - Kenneth
**Falconer**: Fractal Geometry

Mathematical Foundations and Applications - David P.
**Feldman**: Chaos and Fractals

An Elementary Introduction - Gary William
**Flake**: The Computational Beauty of Nature******

Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation - Georg
**Glaeser**, Konrad**Polthier**: Bilder der Mathematik

- visualisation for understanding - Robert
**Goldblatt**: Topoi: The Categorial Analysis of Logic

- category theory as a basis for mathematical logic - Ian
**Hacking**: Why Is There Philosophy of Mathematics At All?

- an informal tour by an experienced guide - Joel David
**Hamkins**: Lectures on the Philosophy of Mathematics******

- from numbers and rigor to incompleteness and set theory - John M.
**Harris**, et al.: Combinatorics and Graph Theory*****

- from the elementary to the infinite - Annette
**Imhausen**: Mathematics in Ancient Egypt

A Contextual History - Stephen H.
**Kellert**: In the Wake of Chaos*****

- what chaos theory is, and what it is not - A.A.
**Kirillov**: A Tale of Two Fractals

- the Sierpinksi and Apollonian gaskets - D.E.
**Knuth**: Surreal Numbers

- a lightly dramatised exploration - Donald E.
**Knuth**: The Art of Computer Programming******

Fundamental Algorithms; Seminumerical Algorithms; Sorting and Searching - Rafail
**Krichevsky**: Universal Compression and Retrieval - Nancy A.
**Lynch**: Distributed Algorithms*****

- for a deep understanding of formal methods - Benoit B.
**Mandelbrot**: The Fractal Geometry of Nature*****

- a casebook and a manifesto - Christopher
**Moore**, Stephan**Mertens**: The Nature of Computation******

- L, P, NP, EXP, co, SPACE, TIME, BPP, BQP, ... - Tristram
**Needham**: Visual Complex Analysis*****

- a genuinely geometric perspective - Heinz-Otto
**Peitgen**, et al.: Chaos and Fractals*****

New Frontiers of Science - Stéphane
**Robin**, et al.: DNA, Words and Models

Statistics of Exceptional Words - Manfred
**Schroeder**: Fractals, Chaos, Power Laws

Minutes from an Infinite Paradise - John
**Stillwell**: Elements of Mathematics: From Euclid to Gödel

- "elementary" and its boundary with "advanced" - John
**Stillwell**: Mathematics and Its History*****

- core ideas of mathematics, in their historical context - Edward R.
**Tufte**: The Visual Display of Quantitative Information*****

- the classic work on statistical graphics - Jeffrey R.
**Weeks**: The Shape of Space*****

- the geometry and topology of surfaces and three-manifolds

**See also**:
computer science