Studying Mathematics

Prepares undergraduate students for the study of mathematics at the university level.
Includes practice exercises that are designed to cultivate the mathematical mind.
Prepares students to develop the necessary skills to understand a mathematics textbook.

Prepares prospective undergraduate students for the study of mathematics Includes practice exercises that are designed to cultivate the mathematical mind Prepares students to develop the necessary skills to study a college math textbook

Auteur

Marco Bramanti is Professor of Mathematics at the Politecnico di Milano. His current research interests include linear second order partial differential equations with nonnegative characteristic form, geometry of Hörmander's vector fields, real analysis, in particular singular integral theory. He has authored numerous research papers, one research monograph, and numerous textbooks.

Giancarlo Travaglini is Professor of Mathematics at the University of Milano-Bicocca. He is the author of numerous research papers and the author or the editor of several books in the areas of abstract harmonic analysis, Fourier analysis, discrepancy theory and mathematics education. His current mathematical interests include Fourier analysis, discrepancy theory, Radon transforms and didactics of mathematics.

Contenu
Part 1. The Language of Mathematics.- A Few Ambiguities of Everyday Language.- To represent by Sets.- Propositions and Properties.- Proofs, Implications and Counterexamples.- Negations and Indirect Proofs.- Formulae and Indices.- Saturation of Indices and Syntactic Consistency of a Formula.- Induction and Natural Numbers.- Part 2. The Study of a Mathematical Book.- To Read a Definition.- To Understand, i.e. to Know How to Reuse.- To Learn How to Correct.- To Sift the Ideas.- To Understand, i.e. to Know How to Explain.- Part 3. Pages and Ideas.- Majorizations.- Uniqueness Proofs (Level B).- Functions and Set Theoretic Arguments.- Tiles, Polyhedra, Characterizations.- Index.