Math for Scientists: Refreshing the Essentials

An Accessible Refresher for Scientific Mathematics

Math for Scientists: Refreshing the Essentials is a practical refresher for anyone who needs to read, understand, and apply mathematical ideas in scientific work. It began as a lecture series for junior neuroscientists with varied backgrounds, and that origin shapes the book: the explanations are gradual, intuitive, and grounded in real research contexts rather than abstract rigor alone.

Core Topics, Revisited with Purpose

Across its chapters, the book revisits the mathematical foundations that often appear in papers, laboratory work, and data analysis. Topics include:

• Numbers and mathematical symbols, including fractions, exponents, logarithms, complex numbers, and conventions for reading formulas
• Equation solving, from linear and quadratic equations to systems of equations, rational and transcendental equations, and inequations
• Trigonometry and Fourier analysis, with attention to angles, trigonometric functions, Euler’s formula, and practical applications
• Vectors and matrices, covering operations, orthogonality, projection, eigenvalues, singular value decomposition, principal component analysis, and independent component analysis
• Limits and derivatives, introducing the ideas behind calculus and how they are used in scientific contexts

A Bridge Between High School Math and Research Practice

The book does not assume that formal mathematics is fresh in your mind. It mixes theory with pen-and-paper exercises and real-world examples, helping readers build intuitive understanding and apply methods such as the General Linear Model, independent component analysis, filtering, medication equivalents, and finding minima of functions. The aim is to make mathematical symbols, equations, and applications feel manageable again.

Who Will Find It Useful

Undergraduate students, PhD students, and researchers in fields that use mathematical principles—neuroscience, biology, psychology, economics, and related disciplines—will find the material relevant. It can be used as a refresher course, for self-study, or as a reference, since most chapters can be read independently. Examples, references, exercises, and solutions support readers who want to work through the material on their own.

Written by Scientists Who Teach Scientists

Natasha Maurits and Branislava Ćurčić-Blake both work at the University Medical Center Groningen. Their backgrounds in mathematics and physics, combined with experience across biophysical chemistry, neurology, psychology, computer science, linguistics, biophysics, and neuroscience, shape the book’s practical, cross-disciplinary approach. The lecture series that inspired the book received positive feedback from participants, and student feedback helped refine the material.

An Invitation to Revisit the Math You Know You Knew

If you have ever stared at a formula in a paper and wished you could recall the basics more clearly, this book was written with you in mind. It offers a structured, friendly path back to mathematical confidence for scientific reading, research, and analysis.