Math for Scientists

Natasha Maurits is professor of Clinical Neuroengineering at the University Medical Center Groningen in the Netherlands. She is an applied mathematician by training and has experience in explaining mathematics to non-mathematicians, from children to adults, for over 25 years. She can explain mathematics in intuitive ways, avoiding formulas as much as possible. This approach is highly valued by her students. Bridging the gap between mathematics and other scientific fields is now her daily bread and butter, working as a mathematician in a hospital, and she enjoys explaining the use and beauty of mathematics.Branislava Ćurčić-Blake works as an Associate Professor in neuroscience and cognitive neuropsychiatry at the University Medical Center Groningen in the Netherlands. She has trained as an experimental physicist (a study with a firm basis in mathematics) and did a PhD in neurobiophysics. Starting as a student and throughout her professional career, she has taught primary, high school, master and PhD students the intricacies of mathematics and physics, often motivating them to study these subjects independently with renewed interest.

• Preface.- Numbers and mathematical symbols: natural, rational, irrational and complex numbers/complex plane: formula reading, often used symbols in mathematical formulas.- Equations: equalities and inequalities: expansions, series: fractional equations: equation solving techniques: various rules (such as Cramer’s rule) to solve equations: introduction to basic functions (e.g. square, square root).- Trigonometry: trigonometric ratios, angles: trigonometric functions (sin, cos, tan) and their complex definitions: epicycles: Fourier series and transform.- Vectors: geometric interpretation of vectors: vector addition/subtraction, scalar multiplication: projections: inner product (including related aspects such as correlation, independence and orthogonality).- Matrices: basic matrix manipulations e.g. multiplication and inversion with examples such as the Jacobian, affine transformation, and rotation: Principal Component analysis in matrix notation.- Differentiation: limits and infinity: continuity of a function: the differential: basic differentiation rules: partial differential equations: introduction to dynamic systems.- Integration: explanation in terms of antiderivatives and area under the curve: basic integration rules: convolution.- statistics.- differential equations.