How to Write Mathematics
Every semester, students who solved the problem still lose the marks: proofs that assume what they promise, inductions with no base case, solutions that never state their answer.
Free · 82 pages (A4) · 123 pages (6 × 9) · DRM-free PDF
This book teaches the skill your courses grade but never teach. Sentence by sentence and proof by proof, it shows exactly where write-ups leak marks, and how to seal every leak, from Tuesday's problem set to your first paper and thesis.
No fluff, and no formulas for writing. Real broken proofs rebuilt line by line, the grader's-eye view of partial credit, and tools you'll use every week of your degree.
What this book helps you do
The six proof shapes, as fill-in writing templates
Eight complete proof makeovers: broken write-ups rebuilt and annotated
Full-marks problem sets and honest partial credit, from the grader's side
A 20-point proof-writing checklist and 40 common errors, catalogued
Ready skeletons for problem sets, papers, and theses
What is inside
The downloadable editions include the complete chapters and toolkit listed below.
The Reader Is Always Right
- Why Good Mathematicians Write Badly
- The Grammar of Mathematics
- Definitions, Statements, and the Anatomy of a Theorem
Proofs
- The Shape of a Proof
- From Scratch Work to Final Draft
- Proof Style
- Proof Makeovers
Problem Sets and Exams
- Solutions That Earn Full Marks
- The Homework System
Papers, Reports, and Theses
- The Architecture of a Mathematical Paper
- Introductions, Abstracts, and Motivation
- Notation, Figures, and Examples
- References and Citation
- Revision: Where Writing Actually Happens
- A Small Paper, Built in Public
Toolkit
- Say It in Words
- The Proof-Writing Checklist
- Forty Common Errors
- Templates
- Further Reading
- Rewrite Workshop and Solutions
Two PDF editions are included
Both layouts are free to download from this page. Use the 6 × 9 edition when you want the paperback reading experience or a compact printout. Use the A4 edition for a larger screen page and easier home or office printing.
A4 screen edition
PDF · 82 pages · 295 KB
A larger page for reading on screen, and the easier one to print at home or in an office.
Download this edition6 × 9 print edition
PDF · 123 pages · 315 KB
The paperback proportions, best when you want a compact printout or the book reading experience.
Download this edition- Title
- How to Write Mathematics
- Subtitle
- Proofs, Papers, and Problem Sets for Students
- Author
- Gaurav Tiwari
- Publisher
- Gaurav Tiwari Publications
- Formats
- 6 × 9 PDF and A4 PDF
- Language
- English
Download How to Write Mathematics
Both editions are free and contain the same complete book. Pick the layout that matches how you read.