Lectures on Differential Geometry (1版)

類似書籍推薦給您

【簡介】 This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry. 【目錄】

Lectures on Probability and Statistics for Graduate-Level Economics

類似書籍推薦給您

【簡介】 Sound knowledge of rigorous probability and statistics methods is essential to pursue graduate studies in economics. These sorts of tools are largely required to conduct research in modern fields of economics such as economic theory, empirical economics, experimental economics, or data science for economics. These notes provide an intuitive roadmap to navigate graduate-level courses in mathematical probability and statistics for economists. Each chapter presents questions prevalent on each topic and lays out the state-of-the-art theoretical frameworks used to address such questions. The book offers a diverse array of solved examples to help gain intuitions on abstract concepts, as well as unsolved exercises to stimulate the readers’ training in such concepts. The book presents the theoretical side of probability and statistics in a rather concise way and stresses the importance of motivating examples and observations. 【目錄】

Lectures on Symmetry-Assisted Computation

類似書籍推薦給您

【簡介】 Scientific problems have an internal "beauty", called, referred to, precisely speaking, as their "symmetry". The symmetry arises, often, from the fact that the scientific problem refers to an object (a molecule, a crystal) and the object itself has some "symmetry" elements, but in more abstract situations, such as those arising in particle physics and quantum technologies, symmetry is often the only known (and relevant!) fact about the problem. The scope of these Lecture Notes is to educate how to recognize the symmetry of a scientific problem and how to use symmetry to understand, manipulate and, finally, solve it. The principle guiding these Lecture Notes is that "learning by doing" is the only way that young students can later become productive in science, business and industry. The lecture Notes have, essentially, two components. The first one reports the content of a set of lectures, held at ETH Zurich at the master and PhD level, frequented mainly by students from the department of Physics, Chemistry and Material Science. The lectures were accompanied by a set of student projects on various scientific subjects related to symmetry. These projects ended with a manuscript, worked out by the students themselves and edited into the second component of these Lecture Notes. 【目錄】 Lectures: Geometrical, Algebraic, and Analytic Aspects of Symmetry Representation Theory of Groups with Average SO3 and the General Method of Infinitesimal Transformations The Symmetry Group of the Operator and Some Practical Applications Point Groups and Space Groups of Crystallography Applications to Solid-State Physics The Relativistic Electronic Structure of Atoms and Solids Young Diagrams and Particle Physics The Permutation Group and Its Applications to Many-Body Problems Group Theory and Phase Transitions Exercises: Exercises to Lecture 1 Exercises to Lecture 2 Exercises to Lecture 3 Exercises to Lecture 4 Exercises to Lecture 5 Projects: Project for Lecture 2: Functional Analytic and Numerical Aspects of Eigenvalue Problems Project for Lecture 4: Symmetry Arguments in Classical Mechanics Project for Lecture 4: Crystal Field Splitting and the Jahn–Teller Effect Project for Lecture 4: Vibrational Modes of the NH3 Molecule Project for Lecture 5: Frieze Patterns Project for Lecture 5: An Algebraic Proof of the Hessel Theorem Project for Lecture 6: Empty-Lattice Band Structure Project for Lecture 6: Symmetry Analysis of Graphene Band Structure and Dirac Cones Project for Lecture 6: Topological Protection by Non-symmorphic Degeneracy Project for Lecture 7: Topological Aspects of Continuous Groups and the Universal Covering Groups Project for Lecture 7: Optical Spin Orientation in Atoms and Solids Project for Lecture 9: Quantum Chemistry