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Notation $x$ in Algebra vs Stats Similarities Represent the value of some quality Variables can be discrete or continuous Can be part of a larger calculation For example, $2x$ could be double the heights of everyone. This is known as [[Stats - Coding]]S . Differences Variables can represent multiple objects, like a set. Can do operations on $x$ like it’s a collection of values: $\sum x$, the sum of all values in $x$ $\bar{x}$, the mean of all values in $x$.

What is uniform acceleration?? Where the acceleration is constant during motion. What is non-uniform acceleration?? Where the acceleration changes during motion. Vector’s quote in Dispicable Me is?? “I commit crimes with both direction and magnitude” Mass is a vector/scalar quantity?? Scalar. Energy is a vector/scalar quantity?? Scalar. Velocity is a vector/scalar quantity?? Vector. Speed is a vector/scalar quantity?? Scalar. Displacement is a vector/scalar quantity?? Vector. Distance is a vector/scalar quantity?? Scalar. How could you describe the velocity of a object moving at a constant speed in a circle?

Forces What is the weight of an object?? The force acting vertically downwards. What is the normal reaction?? The force acting perpindicular from a surface when an object is in contact with the surface. What is the normal reaction the same as?? The weight of an object on a surface. What is the name of the force acting perpindicular from a surface on an object resting on the surface?? The normal reaction. What is friction?? The force which opposed the motion between two rough surfaces.

Models What is a model?? A model is a simplified representation of a physical situation, made by accepting assumptions. What’s an example of a common assumption?? No air resistance Constant gravity Uniform mass What two questions need to be asked when setting up a mathematical model?? What are your assumptions? What are the variables? If the answer presented by a mathematical model is unreasonable, what should be done?? You should reconsider your assumptions.

Boolean Algebra Boolean algebra is like writing algebraic expressions acting on variables. Boolean notation is the set of symbols that define logical operators on variables. $$ P = \text{NOT} (A \text{AND} B) P = \overline{A \cdot B} $$ $$ P = (A \text{AND} B) \text{OR} C P = (A \cdot B) + C $$ NOT $$ P = \text{NOT} A P = \overline{A} $$ What does the notation $\overline{A}$ in boolean algebra?? NOT. AND $$ P = A \text{AND} B P = A \cdot B $$

Argand Diagrams Argand diagrams are a way of representing complex numbers by imagining them as points on a plane. In an Argand diagram: The $x$-axis is the “real” axis The $y$-axis is the “imaginary axis The complex number $z = x + yi$ can be represented on the diagram by the point $P(x, y)$ where $x$ and $y$ are coordinates. In other words: The horizontal position represents the real part of $z$. The vertical position represents the imaginary part of $z$.

Conjugates A pair of complex numbers with a different sign but otherwise the same values are called conjugates: $$ 3 + 4i 3 - 4i $$ What are complex conjugates?? A pair of complex numbers with real and imaginary parts equal in magnitude but opposite in sign: $a+bi$ and $a-bi$ What is a pair of complex numbers $a+bi$ and $a-bi$ called?? A complex conjugate. What is the result of multipling complex conjugates?? You get a real number.

Units and Prefixes Units and Prefixes are a simple topic but very important and foundational for the rest of physics as a whole. It’s one of those things that are important learning because it improves fluency in thought involving physics problems and having a good conceptual understanding of what the units actually represent can also be helpful. Units What are the two types of units?? Base units Compound units What is a base unit?

Logic Gates Name Shape AND Like a “D” OR Like a crescent NOT Like a triangle with a dot NAND Like and with a dot NOR Like an OR with a dot XOR Like OR with an extra crescent AND Input 1 Input 2 Output 0 0 0 0 1 0 1 0 0 1 1 1 OR Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 1 NOT Input 1 Output 0 1 1 0 NAND AND + NOT

This entry focuses on the notes and observations around Michael Nielsen’s essay “Augmenting Long-term Memory”. Introduction Attempts to augment memory using computers have been around for a long time: Memex in 1945. Even the internet itself was due to Tim Berner-Lee’s employer seeking to develop a “collective institutional memory”. Anki is a modern attempt at augmenting memory. “Anki makes memory a choice, rather than a haphazard event, to be left to chance”.

Computing Syllabus Link to specification: https://filestore.aqa.org.uk/resources/computing/specifications/AQA-7516-7517-SP-2015.PDF Entries [[Computing - Operating Systems]]S [[Computing - Logic Gates]]S [[Computing - Boolean Algebra]]S [[Computing - Hardware and Software]]S [[Computing - Translators and Machine Code]]S [[Computing - Libraries]]S [[Computing - Programming Languages]]S [[Computing - Little Man Computer]]S [[Computing - Computer Organisation and Architecture]]S [[Computing - Harvard vs Von Neumann Architecture]]S [[Computing - AQA Assembly]]S [[Computing - Queues]]S [[Computing - Data Representation]]S [[Computing - Binary]]S [[Computing - The Processor]]S [[Computing - Images]]S [[Computing - Sound]]S [[Computing - MIDI]]S [[Computing - Compression]]S [[Computing - Encryption]]S [[Computing - Number Systems]]S [[Computing - Stacks]]S [[Computing - Hash Tables]]S [[Computing - Graphs]]S [[Computing - Trees]]S [[Computing - Vectors]]S [[Computing - SQL]]S [[Computing - Databases]]S [[Computing - Input & Output Devices]]S [[Computing - Object Oriented Programming]]S [[Computing - Finite State Machines]]S [[Computing - Sets]]S [[Computing - Regular Expressions]]S [[Computing - Regular Languages]]S [[Computing - Turing Machines]]S [[Computing - Reverse Polish Notation]]S [[Computing - Backus-Naur Form]]S [[Computing - Parsing]]S [[Computing - Syntax Diagrams]]S [[Computing - Networking]]S [[Computing - Communication]]S [[Computing - Topologies]]S [[Computing - WiFi]]S [[Computing - Cloud Computing]]S [[Computing - Thick and Thin Clients]]S [[Computing - Social and Legal Challenges]]S [[Computing - Structure of the Internet]]S [[Computing - Network Hardware]]S [[Computing - TCP/IP Stack]]S [[Computing - Client/Server Model]]S [[Computing - Functional Programming]]S [[Computing - Big Data]]S [[Computing - Recursion]]S [[Computing - Searching Graphs]]S [[Computing - Limits of Computation]]S [[Computing - Abstraction]]S Syllabus Fundamentals of Programming Programming Data Types Programming Concepts Operations Constants and Variables String-Handling Random Number Generation Exception Handling Subroutines Recursion Programming Paradigms Procedural-oriented programming Object-oriented programming Fundamentals of Data Structures Data Structures and Abstract Data Types Data Structures Arrays Fields, Records and Files Abstract data types/data structures Dictionaries Fundamentals of Algorithms Graph-traversal Tree-traversal Reverse-polish notation Searching Algorithms Sorting Algorithms Optimisation Algorithms Theory of Computation Abstraction and Automation Problem-solving Following and writing algorithms Abstraction Information hiding Procedural abstraction Functional abstraction Data abstraction Problem abstraction Decomposition Composition Automation Regular languages Finite state machines Regular expressions Regular language Context-free languages BNF, Syntax Diagrams Classification of Algorithms Big-O notation Limits of computation Computable and non-computable problems Halting Problem A Model of Computation Turing Machines Data representation Number bases Units of information Bits and bytes Units Binary Unsigned binary Signed binary Binary and fractions Information coding systems ASCII and Unicode Error checking and correction Sound Midi Images Bit patterns Analogue and digital Graphics Bitmapped graphics Vector graphics Compression Encryptions Fundamentals of computer systems Hardware and Software Operating Systems Programming Languages Translators and Machine Code Logic Gates Boolean Algebra Computer Organisation and Architecture Harvard vs Von Neumann Architecture Internal hardware components of a computer The stored program concept Structure and role of the processor External hardware devices I/O devices Secondary storage devices Consequences and uses of computing Moral, social, legal and cultural issues Fundamentals of communication and networking Communication Networking The Internet TCP/IP Protocol Fundamentals of databases Data models and entity relationship modelling Relational databases Database design SQL Client server databases Big Data Fundamentals of functional programming Function Type First-class Objects Functional application Composition of functions Writing functional programs Lists in functional programming Systematic approach to problem solving Aspects of Software Development Analysis Design Implementation Testing Evaluation NEA Info This page was last updated on 2022-02-21.

Further Maths Syllabus Link to specification: https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-further-mathematics-specification.pdf Papers Paper 1 & 2: Core Pure Mathematics Core Pure 1 [[Further Maths - Complex Numbers]]S [[Further Maths - Cubics]]S [[Further Maths - Argand Diagrams]]S [[Further Maths - Conjugates]]S [[Further Maths - Series]]S [[Further Maths - Sums of Natural Numbers]]S [[Further Maths - Series Tips and Tricks]]S [[Further Maths - Sums of Squares]]S [[Further Maths - Sums of Cubes]]S [[Further Maths - Matricies]]S [[Further Maths - Determinants]]S [[Further Maths - Inverting Matricies]]S [[Further Maths - Solving Systems of Equations Using Matricies]]S [[Further Maths - Solving Systems of Equations Using Triangle Method]]S [[Further Maths - Volumes of Revolutions]]S [[Further Maths - Radians]]S [[Further Maths - Roots of Polynomials]]S [[Further Maths - Polar Form]]S [[Further Maths - Trigonometry Values]]S [[Further Maths - Odd and Even Functions]]S [[Further Maths - Loci in the Argand Diagram]]S [[Further Maths - Regions in the Argand Diagram]]S [[Further Maths - Linear Transformations]]S [[Further Maths - Induction]]S [[Further Maths - Induction for Series]]S [[Further Maths - Induction for Divisibility]]S [[Further Maths - Induction for Matricies]]S [[Further Maths - Vectors]]S [[Further Maths - Vector Equation of a Line]]S [[Further Maths - Vector Equation of a Plane]]S [[Further Maths - Dot Product]]S Core Pure 2 [[Further Maths - The Method of Differences]]S [[Further Maths - Partial Fractions]]S [[Further Maths - Maclaurin Series]]S [[Further Maths - Exponential Form of Complex Numbers]]S [[Further Maths - Trig Equations with Complex Numbers]]S [[Further Maths - Roots of Complex Numbers]]S [[Further Maths - Hyperbolic Functions]]S [[Further Maths - Mean Value of a Function]]S [[Further Maths - Improper Integrals]]S [[Further Maths - Integrating and Differentiating Inverse Trig Functions]]S [[Further Maths - Differential Equations]]S [[Further Maths - Coupled Differential Equations]]S Papers 3 & 4: Choices Further Pure 1 [[Further Maths - Inequalities]]S [[Further Maths - Conic Sections]]S [[Further Maths - T-formulae]]S [[Further Maths - Leibnitz's Theorem]]S [[Further Maths - L'Hôpital's Rule]]S [[Further Maths - Weierstrass Substitution]]S [[Further Maths - Taylor Series]]S [[Further Maths - Limits]]S [[Further Maths - Numerical Methods]]S [[Further Maths - Reducible Differential Equations]]S [[Further Maths - Cross Product]]S Decision Mathematics [[Further Maths - Bubblesort]]S [[Further Maths - Shuttlesort]]S [[Further Maths - Bin-packing]]S [[Further Maths - Graphs]]S [[Further Maths - Eulerian Trails]]S [[Further Maths - Hamiltonian Cycles]]S [[Further Maths - Kruskal's Algorithm]]S [[Further Maths - Prim's Algorithm]]S [[Further Maths - Polar Coordinates]]S [[Further Maths - Dijkstra's Algorithm]]S [[Further Maths - Route Inspection]]S [[Further Maths - Travelling Salesperson Problem]]S Info This page was last updated on 2022-02-21.