Jaume Aguadé (Barcelona, 1953) was a full professor in the Department of Mathematics at the Universitat Autònoma de Barcelona for 34 years. His research has focused on algebraic topology and the homotopy theory of Lie groups. He has also been deeply committed to teaching and has authored several books that reflect his personal approach to mathematics education, including Notes on Elementary Topology, Mathematics and Modelling for Environmental Sciences, A Course in Linear Geometry, and the present volume. Now retired, he is currently working on a book on compact Lie groups, provisionally titled Groups Worth Meeting. Beyond mathematics, he has been an enthusiastic practitioner of hiking, mountaineering, and ski touring—activities that in recent years he has replaced with road cycling.

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• Part I-Logic, Numbers, and Structure of Mathematical Discourse.- Propositional Logic.- First-Order Logic.- The Natural Numbers: Peano's Axioms and Induction.- The Natural Numbers: Recursion.- Mathematical Discourse.- Gödel's Theorems.- Exercises on Logic and Natural Numbers.- Part II-Set Theory.- The ZFC Axioms.- Products, Relations, Functions.- The Quotient Set.- Finite, Infinite, Infinities.- Exercises on Sets and Functions.- Part III-A Glimpse into Group Theory.- Permutations.- The Concept of a Group.- The Alternating Group.- Conjugation, Normal Subgroups and Kernels.- The Cube Group.- Exercises on Groups.- Part IV-Arithmetic.- The Integers and the Rationals.- Divisibility.- Z is a PID.- The Prime Numbers.- Modular Arithmetic.- The Rings Z/(m) and the Finite Fields.- Euler's phi function.- Public-Key Cryptography.- Exercises on Arithmetic.- Part V: Polynomials.- Polynomials: Basic Concepts.- k|x| Closely Resembles Z.- Multiplicity, Irreducible Polynomials and Roots of Unity.- Solving Polynomials Equations.- Every Nonconstant Polynomial Has a Root.- Exercises on Polynomials.- Part VI-Complex Numbers.- Three Definitions of the Complex Numbers.- The Fundamental Theorem of Algebra.- The Most Beautiful Formula: e^in+1=0.- Exercises on Complex Numbers.- Index.

Jaume Aguadé (Barcelona, 1953) was a full professor in the Department of Mathematics at the Universitat Autònoma de Barcelona for 34 years. His research has focused on algebraic topology and the homotopy theory of Lie groups. He has also been deeply committed to teaching and has authored several books that reflect his personal approach to mathematics education, including Notes on Elementary Topology, Mathematics and Modelling for Environmental Sciences, A Course in Linear Geometry, and the present volume. Now retired, he is currently working on a book on compact Lie groups, provisionally titled Groups Worth Meeting. Beyond mathematics, he has been an enthusiastic practitioner of hiking, mountaineering, and ski touring—activities that in recent years he has replaced with road cycling.

Select Guide Rating

• Part I-Logic, Numbers, and Structure of Mathematical Discourse.- Propositional Logic.- First-Order Logic.- The Natural Numbers: Peano's Axioms and Induction.- The Natural Numbers: Recursion.- Mathematical Discourse.- Gödel's Theorems.- Exercises on Logic and Natural Numbers.- Part II-Set Theory.- The ZFC Axioms.- Products, Relations, Functions.- The Quotient Set.- Finite, Infinite, Infinities.- Exercises on Sets and Functions.- Part III-A Glimpse into Group Theory.- Permutations.- The Concept of a Group.- The Alternating Group.- Conjugation, Normal Subgroups and Kernels.- The Cube Group.- Exercises on Groups.- Part IV-Arithmetic.- The Integers and the Rationals.- Divisibility.- Z is a PID.- The Prime Numbers.- Modular Arithmetic.- The Rings Z/(m) and the Finite Fields.- Euler's phi function.- Public-Key Cryptography.- Exercises on Arithmetic.- Part V: Polynomials.- Polynomials: Basic Concepts.- k|x| Closely Resembles Z.- Multiplicity, Irreducible Polynomials and Roots of Unity.- Solving Polynomials Equations.- Every Nonconstant Polynomial Has a Root.- Exercises on Polynomials.- Part VI-Complex Numbers.- Three Definitions of the Complex Numbers.- The Fundamental Theorem of Algebra.- The Most Beautiful Formula: e^in+1=0.- Exercises on Complex Numbers.- Index.