A-LEVEL MATHS TUTOR,revise A-level maths.Your guide for effective advanced maths revision. Multiplicative inverse Number which when multiplied by x equals 1 The term reciprocal was in common use at least as far back as the third edition of Encyclopædia Britannica (1797) to describe two numbers whose product is 1; geometrical quantities in inverse proportion are described as reciprocall in a 1570 translation of Euclid's Elements.[1] In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse). The notation f −1 is sometimes also used for the inverse function of the function f, which is for most functions not equal to the multiplicative inverse. Examples and counterexamples[edit] In modular arithmetic, the modular multiplicative inverse of a is also defined: it is the number x such that ax ≡ 1 (mod n). The sedenions are an algebra in which every nonzero element has a multiplicative inverse, but which nonetheless has divisors of zero, that is, nonzero elements x, y such that xy = 0. where Complex numbers[edit] . and .
Brookhaven Maths - A level Core Maths Notes These notes are based on the class notes I made during my pure maths A Level course. They have been transcibed onto the computer and saved as a zipped pdf file. The notes should be ideal for A-level maths core revision and are based mainly on the OCR syllabus, with a touch of AQA. The notes contain many worked examples, which should give a good overview of the many techniques required. C1 to C4 - Core A Level Maths Revision & Class Notes: All my notes have been combined into one pdf file. Due to exceeding our bandwidth limits the file has been moved to another server, but can still be downloaded via the 'download' button here. The downloaded file is a zip file, ALevelNotesC1C4.zip. Unzip to extract the latest version of the pdf document Updates Please check back for further updates to the C1 / C2 / C3 / C4 Core A Level maths revision notes. Updated Sections are marked in the contents list at the beginning of each Core module. Previous Updates to C1-C4:
Introduction to Higher Mathematics by Department of Mathematics Whitman College This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. This text was initially written by Patrick Keef and modified by David Guichard. This HTML version was produced using a script written by David Farmer and adapted by David Guichard. Please report problems to guichard@whitman.edu.
Concepts of Mathematics - Summer I 2012 Announcements Friday 5/25/12: The LaTeX tutorial will be Tuesday May 29 at 5-6:30ish pm in Wean 5207Sunday 5/20/12: Course calendar is settled (as far as I know!). Homework 1 is up as well, and notes for the first day. Notes for the second and third day should be done before class tomorrow.Thursday 5/17/12: Syllabus is finalized. I am still messing with the course calendar though. It will be settled as far as I know by the beginning of the course Course Summary Welcome to Concepts of Mathematics. The first part of the course will be on logic and proof techniques. The second part of the course will cover structures on sets. The third part of the course will be on discete math. This course, especially over the summer when the time to teach is cut in more than half, is very intense.
Proofs from The Book - The most elegant axioms, theorems, and proofs in school mathematics. Math 3005 - A Transition to Higher Mathematics TextbookThe 2nd edition of Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. Solutions to Selected Homework ProblemsBelow you will find links to the solutions of some of the homework exercises that have been assigned. Chapter 3: Direct Proof and Proof by Contrapositive Chapter 4: More on Direct Proof and Proof by Contrapositive Chapter 5: Existence and Proof by Contradiction Chapter 6: Mathematical Induction Chapter 7: Prove or DisprovePlease review this section on your own. Chapter 8: Equivalence Relations
Fundamentals of mathematics Catalog Record: Fundamentals of mathematics | Hathi Trust Digital Library Navigation HathiTrust Digital Library Search this index Main Content Similar Items An introduction to modern mathematics By: Vance, Elbridge Putnam, 1915- Published: (1963) Generalizations of non-alternating and non-separating transformations / By: Vance, Elbridge Putnam, 1915- Published: (1940) Unified algebra and trigonometry. Tools Fundamentals of mathematics. Viewability: Full view (original from University of California) Search Catalog Search Bibliographic search (Title, Author, Subject, ISBN/ISSN, Publisher, Series Title, or Year of Publication) of all HathiTrust items Experimental Search Full-text search of a small subset of HathiTrust items Build & View Custom Collections Go to Public Collections to browse other people's collections. Full-text searching is available within public or private collections, and within individual items. Close Search Tips Phrase Searching Use quotes to search an exact phrase: e.g.
A brief introduction to the infinitesimal... Catalog Record: A brief introduction to the infinitesimal calculus. Designed especially to aid in reading mathematical economics and statistics | Hathi Trust Digital Library Navigation HathiTrust Digital Library Search this index Main Content Similar Items Tools A brief introduction to the infinitesimal calculus. Viewability: Full view (original from University of California) Search Catalog Search Bibliographic search (Title, Author, Subject, ISBN/ISSN, Publisher, Series Title, or Year of Publication) of all HathiTrust items Experimental Search Full-text search of a small subset of HathiTrust items Build & View Custom Collections Go to Public Collections to browse other people's collections. Full-text searching is available within public or private collections, and within individual items. Close Search Tips Phrase Searching Use quotes to search an exact phrase: e.g. Wildcards Use * or ? Boolean Searching Use AND and OR between words to combine them with Boolean logic: e.g.