Math That Makes You Go Wow
by M. Boittin, E. Callahan, D. Goldberg, J. Remes
Publisher: Ohio State University 1998
This is an innovative project by a group of Yale undergraduates: A Multi-Disciplinary Exploration of Non-Orientable Surfaces. The course is designed to be included as a short segment in a late middle school or early high school math course.
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by Andrew Ranicki - Springer
This book is an introduction to high-dimensional knot theory. It uses surgery theory to provide a systematic exposition, and it serves as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
by Andrew Ranicki - Oxford University Press
Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.
by David Bachman - arXiv
This is a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students.
by Nigel Hitchin
Geometry of Surfaces by Nigel Hitchin is a textbook on surfaces. However the author is also going to try and consider surfaces intrinsically, or abstractly, and not necessarily embedded in three-dimensional Euclidean space.