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e-book
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Logic Symbolic mathematical Textbooks
- Resource Type:
- e-book
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e-book
"Essential skills are used in every job to varying degrees and at different levels of complexity. They provide the foundation for learning all other skills and enable people to evolve in their jobs and adapt to changes in the workplace. The following list of lines and competencies was generated with the goal of creating an entry-level trades training resource, while still offering the flexibility for lines to be used as stand-alone books"--BC Campus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Geometry
- Resource Type:
- e-book
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Courseware
The focus of this course: - Applications of topology in condensed matter based on bulk-edge correspondence. - Special attention to the most active research topics in topological condensed matter: theory of topological insulators and Majorana fermions, topological classification of “grand ten” symmetry classes, and topological quantum computation - Extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.
- Keywords:
- Condensed matter Topology
- Resource Type:
- Courseware
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Others
In this learning activity you'll review the structure and function of the different tissues of the human body.
- Subjects:
- Health Sciences and Human Biology
- Keywords:
- Human anatomy Human physiology
- Resource Type:
- Others
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Video
Mohamad Jebara loves mathematics -- but he's concerned that too many students grow up thinking that this beautiful, rewarding subject is difficult and boring. His company is experimenting with a bold idea: paying students for completing weekly math homework. He explores the ethics of this model and how it's helping students -- and why learning math is crucial in the era of fake news.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Study teaching
- Resource Type:
- Video
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e-book
Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Textbooks Statistics -- Computer programs
- Resource Type:
- e-book
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e-book
Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Bayesian statistical decision theory Python (Computer program language) Textbooks
- Resource Type:
- e-book
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e-book
Thermodynamics and Chemistry is designed primarily as a textbook for a one-semester course in classical chemical thermodynamics at the graduate or undergraduate level. It can also serve as a supplementary text and thermodynamics reference source.
- Subjects:
- Chemistry
- Keywords:
- Thermodynamics Chemistry Textbooks
- Resource Type:
- e-book
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Others
In this animated object, learners examine how thermal energy is transferred by conduction, convection, and radiation. A brief quiz completes the activity.
- Subjects:
- Physics
- Keywords:
- Heat -- Transmission
- Resource Type:
- Others
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Video
Between you and the rest of the world lies an interface that makes up 16% of your physical weight. This is your skin, the largest organ in your body: laid out flat, it would cover close to 1.7 square metres of ground. But besides keeping your organs in, what is its purpose? Emma Bryce takes us into the integumentary system to find out. Lesson by Emma Bryce, animation by Augenblick Studios.
- Course related:
- BME1D04 Subject Title Skin-Care Technologies: Principles, Applications and Safety
- Subjects:
- Health Sciences and Human Biology
- Keywords:
- Body covering (Anatomy) Skin
- Resource Type:
- Video
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Video
Consider the following sentence: "This statement is false." Is that true? If so, that would make the statement false. But if it's false, then the statement is true. This sentence creates an unsolvable paradox; if it's not true and it's not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel's Incompleteness Theorem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Incompleteness theorems Gödel's theorem
- Resource Type:
- Video
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Others
Euclid’s Elements was a collection of 13 books about geometry originally written circa 300 BC. Shortly after the advent of the printing press, many editions and translations have been created over the centuries. Byrne’s 1847 edition of the first six books stands out for its unique use of colorful illustrations to demonstrate proofs rather than using letters to label angles, edges, and shapes. His edition was one of the first books to be published with such detailed use of colors and combined with its detailed diagrams makes it an impressive feat of publishing for the times and it stands out even today as a work of art. This site is a reproduction of Byrne’s Euclid by Oliver Byrne from 1847 that pays tribute to the beautiful original design and includes enhancements such as interactive diagrams, cross references, and posters designed by Nicholas Rougeux.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Euclid's Elements Elements (Euclid) Geometry
- Resource Type:
- Others
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Video
Masterpieces of microengineering, kinesins are motorized transport machines that move cellular materials to their correct locations in the cell so they can perform their functions. Kinesins have two feet, or "globular heads," that literally walk, one foot over another. Known as the "workhorses of the cell," kinesins can carry cargo many times their own size.
- Course related:
- ABCT2103 Cell Biology
- Subjects:
- Biology
- Keywords:
- Kinesin
- Resource Type:
- Video
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Others
Learners read a brief description of the vertebral column and examine the distinctive features of the cervical, thoracic, and lumbar vertebrae.
- Subjects:
- Health Sciences, Rehabilation Science, and Biology
- Keywords:
- Spine -- Anatomy
- Resource Type:
- Others
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Others
Learners play a vascular system "game" to identify the arteries, capillaries, and veins that make up the renal blood supply pathway. A score is given at the end of the activity.
- Subjects:
- Health Sciences and Human Biology
- Keywords:
- Kidneys -- Physiology Kidneys -- Blood vessels
- Resource Type:
- Others
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Video
In this screencast, learners examine the function and location of the motor neurons and the damage that can result when they are injured.
- Subjects:
- Health Sciences, Rehabilitation Science, and Biology
- Keywords:
- Motor neurons Brain -- Anatomy
- Resource Type:
- Video
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Video
Origami, which literally translates to "folding paper," is a Japanese practice dating back to at least the 17th century. In origami, a single, traditionally square sheet of paper can be transformed into almost any shape, purely by folding. The same simple concepts yield everything from a paper crane with about 20 steps, to a dragon with over 1,000 steps. Evan Zodl explores the ancient art form.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Origami -- Mathematics
- Resource Type:
- Video
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Video
Physicist Werner Heisenberg said, "When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first." As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks. Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work.
- Subjects:
- Physics
- Keywords:
- Turbulence Starry night (Gogh Vincent van)
- Resource Type:
- Video
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Others
In this interactive object, learners examine the neuron pathway into and out of the spinal cord. They complete the activity by testing their knowledge of vocabulary and the location of spinal cord structures.
- Subjects:
- Health Sciences and Human Biology
- Keywords:
- Knee jerk
- Resource Type:
- Others
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Video
Hydrogen fuel cell cars and lithium-ion battery powered cars, which is more energy efficient and cost effective? This video shows you some facts from perspectives of production, storage of fuels, and infrastructure set up for charging.
- Subjects:
- Electrical Engineering, Chemistry, Environmental Engineering, and Transportation
- Keywords:
- Hydrogen cars Hydrogen as fuel Electric vehicles Fuel cells Hydrogen -- Storage
- Resource Type:
- Video