Topic 5 - Miami-Dade County Public Schools
... 2. Formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables. 3. Analyzing and performing operations on these relationships to draw conclusions. 4. Interpreting the results of the mathemati ...
... 2. Formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables. 3. Analyzing and performing operations on these relationships to draw conclusions. 4. Interpreting the results of the mathemati ...
Foundation
... What students should know ● Use priority of operations with positive and negative numbers. ● Simplify calculations by cancelling. ● Use inverse operations. ● Round to a given number 1.2 Decimal numbers of decimal places. ● Multiply and divide decimal numbers. ● Write decimal numbers of 1.3 Place val ...
... What students should know ● Use priority of operations with positive and negative numbers. ● Simplify calculations by cancelling. ● Use inverse operations. ● Round to a given number 1.2 Decimal numbers of decimal places. ● Multiply and divide decimal numbers. ● Write decimal numbers of 1.3 Place val ...
Fermat`s Last Theorem - Math @ McMaster University
... This proof makes use of a technique, called the method of infinite descent, introduced by Fermat. We start with the assumption that x, y , and w are positive integers that satisfy the equation such that w is as small as possible amongst all of the positive integer solutions to the equation. We then ...
... This proof makes use of a technique, called the method of infinite descent, introduced by Fermat. We start with the assumption that x, y , and w are positive integers that satisfy the equation such that w is as small as possible amongst all of the positive integer solutions to the equation. We then ...
Lecture Notes - School of Mathematics
... 13 lectures: Sets. Definition, subsets, simple examples, union, intersection and complement. De Morgan’s Laws. Elementary Logic; universal and existential qualifiers. Proof by contradiction and by induction. 9 lectures: Methods of proof for inequalities. Solution of inequalities containing unknown v ...
... 13 lectures: Sets. Definition, subsets, simple examples, union, intersection and complement. De Morgan’s Laws. Elementary Logic; universal and existential qualifiers. Proof by contradiction and by induction. 9 lectures: Methods of proof for inequalities. Solution of inequalities containing unknown v ...
Lesson 7
... a. Suppose we are to play the 4-number game with the symbols a, b, c, and d to represent numbers, each used at most once, combined by the operation of addition ONLY. If we acknowledge that parentheses are not needed, show there are essentially only 15 expressions one can write. ...
... a. Suppose we are to play the 4-number game with the symbols a, b, c, and d to represent numbers, each used at most once, combined by the operation of addition ONLY. If we acknowledge that parentheses are not needed, show there are essentially only 15 expressions one can write. ...
Arithmetic in Metamath, Case Study: Bertrand`s Postulate
... the “multiplication table” for base 10 would require many more basic facts like 7 · 8 = 10 · 5 + 6, while the multiplication table of base 4 requires only numbers as large as 9, which fits inside our available collection of basic facts. Furthermore, within this constraint a large base allows for sho ...
... the “multiplication table” for base 10 would require many more basic facts like 7 · 8 = 10 · 5 + 6, while the multiplication table of base 4 requires only numbers as large as 9, which fits inside our available collection of basic facts. Furthermore, within this constraint a large base allows for sho ...
4.4 Matrices: Basic Operations
... and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column of numbers. If the numbe ...
... and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column of numbers. If the numbe ...
Co-ordinate Geometry
... In general, co-ordinates of a point P(x, y) imply that distance of P from the y-axis is x units and its distance from the x-axis is y units. You may note that the co-ordinates of the origin O are (0, 0). The y co-ordinate of every point on the x-axis is 0 and the x co-ordinate of every point on the ...
... In general, co-ordinates of a point P(x, y) imply that distance of P from the y-axis is x units and its distance from the x-axis is y units. You may note that the co-ordinates of the origin O are (0, 0). The y co-ordinate of every point on the x-axis is 0 and the x co-ordinate of every point on the ...
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term ""mathematics"" from the ancient Greek μάθημα (mathema), meaning ""subject of instruction"". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Chinese mathematics made early contributions, including a place value system. The Hindu-Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and were transmitted to the west via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.