This is a textbook for first year Computer Science. Algorithms and Data Structures With Applications to Graphics and Geometry.

This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the concepts, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Seminar on a selected topic from Renaissance architecture. Requires original research and presentation of a report. The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.

The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.

The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.

This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.

t is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

Based on knowledge of the unit Circles, students see how sinusoids (Sine and coSine waves) get their shapes.

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.

This site teaches High Schoolers how to express geometric properties with equations through a series of 1721 questions and interactive activities aligned to 12 Common Core mathematics skills.

This site teaches High Schoolers Geometric Measurement and Dimension through a series of 82 questions and interactive activities aligned to 4 Common Core mathematics skills.

This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

This site teaches High Schoolers how to Interpret Categorical and Quantitative Data through a series of 45 questions and interactive activities aligned to 2 Common Core mathematics skills.

Explore the world of lines. Investigate the relationships between linear equations, slope, and graphs of lines. Challenge yourself in the line game!

These problems are designed to be completed in class by students (in groups or solo) with discussion to make the class more active.

Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.