Mathematics Applications and Interpretation for the IB Diploma Higher Level provides comprehensive coverage of the new curriculum, developed for first examinations in 2021. Written by a highly experienced IB author team, this book includes the following features: integrated GeoGebra applets created specifically for the course, worked examples to help you tackle questions and apply concepts and skills, practice questions to help you prepare for the exam, a rich and wide-ranging Theory of Knowledge chapter, and guidance on the Internal Assessment.

Analysis in singular spaces is becoming an increasingly important area of research, with motivation coming from the calculus of variations, PDEs, geometric analysis, metric geometry and probability theory, just to mention a few areas. In all these fields, the role of measure theory is crucial and an appropriate understanding of the interaction between the relevant measure-theoretic framework and the objects under investigation is important to a successful research. The aim of this book, which gathers contributions from leading specialists with different backgrounds, is that of creating a collection of various aspects of measure theory occurring in recent research with the hope of increasing interactions between different fields. List of contributors: Luigi Ambrosio, Vladimir I. Bogachev, Fabio Cavalletti, Guido De Philippis, Shouhei Honda, Tom Leinster, Christian Leonard, Andrea Marchese, Mark W. Meckes, Filip Rindler, Nageswari Shanmugalingam, Takashi Shioya, and Christina Sormani.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

The study of ecological systems is often impeded by components that escape perfect observation, such as the trajectories of moving animals or the status of plant seed banks. These hidden components can be efficiently handled with statistical modeling by using hidden variables, which are often called latent variables. Notably, the hidden variables framework enables us to model an underlying interaction structure between variables (including random effects in regression models) and perform data clustering, which are useful tools in the analysis of ecological data. This book provides an introduction to hidden variables in ecology, through recent works on statistical modeling as well as on estimation in models with latent variables. All models are illustrated with ecological examples involving different types of latent variables at different scales of organization, from individuals to ecosystems. Readers have access to the data and R codes to facilitate understanding of the model and to adapt inference tools to their own data.

Containing case studies and examples, the book aims to cover extensive research particularly on surface stress and topics related to the variational approach to the subject, and non-standard topics such as the rigorous treatment of constraints and a full discussion of algebraic inequalities associated with realistic material behaviour, and their implications. Serving as an introduction to the basic elements of Finite Elasticity, this textbook is the cornerstone for any graduate-level on the topic, while also providing a template for a host of theories in Solid Mechanics.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite- and infinite-dimensional representations in classical types and subvarieties of flag varieties and their singularities. Associated varieties and characteristic cycles are covered as well and Kazhdan-Lusztig polynomials are treated. The coverage concludes with a discussion of pattern avoidance and singularities and some recent results on Springer fibers.

In today’s data-driven world, maths is a weapon wielded by banks, insurance companies, tech firms, and government agencies. These organizations use sophisticated algorithms to calculate odds, make predictions, uncover patterns, manage risk, and optimize actions. And they treat you as another number to crunch along the way.

Robin Hood Maths explains the mathematical methods these companies and agencies use to manipulate and profit off of you. It’s easy to assume these algorithms are too complex to even understand, let alone use for yourself. But maths professor Noah Giansiracusa makes the compelling case that anyone can use these same methods, without any special training or advanced knowledge. He offers simple hacks and streamlined formulas for beating the number crunchers at their own game.

With Professor Giansiracusa as your guide, you’ll learn how to use maths to rescue your credit score and make better investments, take control of your social media, and reclaim agency over the decisions you make every day. In a society designed to take from the poor and give to the rich, maths has the potential to be a powerful democratizing force. Robin Hood Maths gives you the tools you need to think for yourself, act in your own best interest, and thrive.