Mathematics: From the Birth of Numbers
A gently guided, profusely illustrated Grand Tour of the world of mathematics.
This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. Over 1000 technical illustrations and cartoons and drawings
Why Read This Book
You should read this book if you want a wide-ranging, reader-friendly refresher of the mathematical ideas that underpin DSP — presented with historical context and plentiful illustrations to build intuition. It won't teach DSP algorithms directly, but it will strengthen your understanding of calculus, linear algebra, probability and differential equations so you can approach signal-processing theory with more confidence.
Who Will Benefit
Early-career engineers or experienced practitioners who need a clear, intuitive review of the mathematical foundations that underpin DSP and signal-processing theory.
Level: Beginner — Prerequisites: Basic high-school algebra and trigonometry are helpful; no advanced mathematics required.
Key Takeaways
- Explain the historical development and meaning of numbers and basic mathematical notation.
- Use calculus and differential equations to formulate and reason about continuous-time problems.
- Apply core linear algebra concepts (vectors, matrices, determinants) that underlie many DSP methods.
- Understand probability basics and elementary statistics relevant to stochastic signal models.
- Interpret complex numbers, series, and transforms at a level that supports later study of Fourier analysis.
Topics Covered
- Numbers and the Birth of Arithmetic
- Fractions, Decimals, and Number Systems
- Elementary Algebra and Polynomials
- Geometry and Trigonometry
- Functions and Graphs
- Calculus: Differentiation and Integration
- Infinite Series and Approximation
- Complex Numbers and Complex Functions
- Matrices, Determinants, and Linear Algebra
- Differential Equations and Applications
- Probability and Elementary Statistics
- Logic, Sets, and Mathematical Foundations
- Topology, Fractals, and Selected Byways
- Historical Notes and Biographical Sketches
How It Compares
Much more accessible and historically oriented than Concrete Mathematics (Graham, Knuth & Patashnik); broader and less encyclopedic or essay-driven than The Princeton Companion to Mathematics.
