Welcome to grade 8 classroom Home room teacher: Michael Marchenko

Math Curriculum Students are required to master the following math topics: Algebra Number Geometry Measures Statistics

Science Curriculum Students are required to master the following science topics: Physics Chemistry Biology Environmental Science Anatomy

What are you the most interested in Math and Science?

Why do you like Math and Science?

Good test scores? Fun? Careers?

Here are the specific topics to study

Geometry GeometryAncient Greek: γεωμετρία; geo- "earth", - metria "measurement is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Algebra Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.

Statistics Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.

Physics Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.

Chemistry Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds.

Biology Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines.

Lets surf some very exciting topics in Math and Science

Higgs boson The Higgs boson or Higgs particle is a proposed elementary particle in the Standard Model of particle physics. The Higgs boson is named after Peter Higgs who, along with others, proposed the mechanism that predicted such a particle in The existence of the Higgs boson and the associated Higgs field explain why the other massive elementary particles in the standard model have their mass.

Higgs boson

Proof of Poincaré conjecture In mathematics, the Poincaré conjecture ( /pw ɛ n.k ɑːˈ re ɪ / pwen-kar-ay; French: [pw ɛ ̃ka ʁ e])[1] is a theorem about the characterization of the three dimensional sphere (3-sphere), which is the hypersphere that bounds the unit ball in four-dimensional space.

Proof of Poincaré conjecture The conjecture states:Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

Proof of Poincaré conjecture

Teleportation Teleportation is the transfer of matter from one point to another without traversing the physical space between them, similar to the concept apport, an earlier word used in the context of spiritualism

Teleportation

Quantum Teleportation Quantum teleportation, or entanglement- assisted teleportation, is a process by which a qubit (the basic unit of quantum information) can be transmitted exactly (in principle) from one location to another, without the qubit being transmitted through the intervening space.

Big Bang The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the Universe to cool and resulted in its present continuously expanding state.

Big Bang

String Theory String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything (TOE), a self-contained mathematical model that describes all fundamental forces and forms of matter.

String Theory

M-Theory

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physicist with a focus on mathematical physics who is a professor of Mathematical Physics at the Institute for Advanced Study. Witten is a researcher in superstring theory, a theory of quantum gravity, supersymmetric quantum field theories and other areas of mathematical physics.

Dirac equation the Dirac equation[1] is a wave equation, formulated by British physicist Paul Dirac in 1928 It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and made relativistic corrections to quantum mechanics.

Schrödinger equation The Schrödinger equation is an equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.

Quantum mechanics Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physics dealing with physical phenomena where the action is on the order of the Planck constant. Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. QM provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter.

Einstein Albert Einstein (14 March 1879 – 18 April 1955) was a German theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics. Einstein is generally considered the most influential physicist of the 20th century. While best known for his mass–energy equivalence formula E = mc 2 (which has been dubbed "the world's most famous equation) he received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect. The latter was pivotal in establishing quantum theory within physics.

Uncertainty principle In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental lower bound on the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. [1] The original heuristic argument that such a limit should exist was given by Werner Heisenberg in A more formal inequality relating the standard deviation of position σ x and the standard deviation of momentum σ p was derived by Kennard[2] later that year (and independently by Weyl[3] in 1928),

Invariant (physics) in mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation. examples of a physical invariant is the speed of light under a Lorentz transformation [1] and time under a Galilean transformation. Such spacetime transformations represent shifts between the reference frames of different observers, and so by Noether's theorem invariance under a transformation represents a fundamental conservation law. For example, invariance under translation leads to conservation of momentum, and invariance in time leads to conservation of energy.

Group theory In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced tremendous advances and have become subject areas in their own right.

Nuclear power

Hydroelectric power

Wind power

Sustainable development Sustainable development (SD) is a pattern of economic growth in which resource use aims to meet human needs while preserving the environment so that these needs can be met not only in the present, but also for generations to come (sometimes taught as ELF- Environment, Local people, Future The term 'sustainable development' was used by the Brundtland Commission which coined what has become the most often-quoted definition of sustainable development as development that "meets the needs of the present without compromising the ability of future generations to meet their own needs."[1][2]

Natural environment The natural environment encompasses all living and non-living things occurring naturally on Earth or some region thereof. It is an environment that encompasses the interaction of all living species.[1] The concept of the natural environment can be distinguished by components:Complete ecological units that function as natural systems without massive human intervention, including all vegetation, microorganisms, soil, rocks, atmosphere and natural phenomena that occur within their boundaries.Universal natural resources and physical phenomena that lack clear-cut boundaries, such as air, water, and climate, as well as energy, radiation, electric charge, and magnetism, not originating from human activity.

Tsunami

Earthquake

Tropical cyclone A tropical cyclone is a storm system characterized by a low- pressure center and numerous thunderstorms that produce strong winds and heavy rain. Tropical cyclones strengthen when water evaporated from the ocean is released as the saturated air rises, resulting in condensation of water vapor contained in the moist air. They are fueled by a different heat mechanism than other cyclonic windstorms such as nor'easters, European windstorms, and polar lows. The characteristic that separates tropical cyclones from other cyclonic systems is that at any height in the atmosphere, the center of a tropical cyclone will be warmer than its surroundings; a phenomenon called "warm core" storm systems.

Newton's laws of motion Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces. They have been expressed in several different ways over nearly three centuries,[1] and can be summarized as follows:First law: Every object continues in its state of rest, or of uniform motion in a straight line, unless compelled to change that state by external forces acted upon it. [2][3][4]Second law: The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma.Third law: When two bodies interact by exerting force on each other, these action and reaction forces are equal in magnitude, but opposite in direction.

Electromagnetism Electromagnetism is the branch of science concerned with the forces that occur between electrically charged particles. In electromagnetic theory these forces are explained using electromagnetic fields. Electromagnetic force is one of the four fundamental interactions in nature, the other three being the strong interaction, the weak interaction and gravitation. Electromagnetism is the interaction responsible for practically all the phenomena encountered in daily life, with the exception of gravity. Ordinary matter takes its form as a result of intermolecular forces between individual molecules in matter. Electrons are bound by electromagnetic wave mechanics into orbitals around atomic nuclei to form atoms, which are the building blocks of molecules. This governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, which are in turn determined by the interaction between electromagnetic force and the momentum of the electrons.

Maxwell's equations Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations have two major variants. The "microscopic" set of Maxwell's equations uses total charge and total current including the difficult-to-calculate atomic level charges and currents in materials. The "macroscopic" set of Maxwell's equations defines two new auxiliary fields that can sidestep having to know these 'atomic' sized charges and currents.

Computer programming Computer programming (often shortened to programming or coding) is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a set of instructions that computers use to perform specific operations or to exhibit desired behaviors. The process of writing source code often requires expertise in many different subjects, including knowledge of the application domain, specialized algorithms and formal logic.

Computer programming

Cryptography Cryptography (or cryptology; from Greek κρυπτός, "hidden, secret"; and γράφειν, graphein, "writing", or - λογία, -logia, "study", respectively)[1] is the practice and study of techniques for secure communication in the presence of third parties (called adversaries).[2] More generally, it is about constructing and analyzing protocols that overcome the influence of adversaries[3] and which are related to various aspects in information security such as data confidentiality, data integrity, and authentication.[4] Modern cryptography intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.

Prime number A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. This theorem requires excluding 1 as a prime.The property of being prime is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n. Algorithms that are much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for primes of special forms, such as Mersenne primes. As of 2011, the largest known prime number has nearly 13 million decimal digits.

Game theory Game theory is the study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."[1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory.[2] Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, to include both human and non-humans, like computers. Classic uses include a sense of balance in numerous games, where each person has found or developed a tactic that cannot successfully better his results, given the other approach.

Prisoner's dilemma The prisoner's dilemma is a canonical example of a game analyzed ingame theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992). A classic example of the prisoner's dilemma (PD) is presented as follows:Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar dealif one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the one that remains silent receives the full one- year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?

Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.

Fermat's Last Theorem In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two.This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult mathematical problems".

Fourier series In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex exponentials). The study of Fourier series is a branch of Fourier analysis.The Fourier series is named in honour of Joseph Fourier (1768–1830), who made important contributions to the study of trigonometric series, after preliminary investigations by Leonhard Euler, Jean le Rond d'Alembert, and Daniel Bernoulli. Fourier introduced the series for the purpose of solving the heat equation in a metal plate, publishing his initial results in his 1807 Mémoire sur la propagation de la chaleur dans les corps solides (Treatise on the propagation of heat in solid bodies), and publishing his Théorie analytique de la chaleur in Early ideas of decomposing a periodic function into the sum of simple oscillating functions date back to the 3rd century BC, when ancient astronomers proposed an empiric model of planetary motions, based on deferents and epicycles.

Trigonometry Trigonometry Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying. Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.

Trigonometry

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

Pythagorean theorem

Tessellation Tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher, who was inspired by studying the Moorish use of symmetry in the Alhambra tiles during a visit in Tessellations are seen throughout art history, from ancient architecture to modern art.In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.[1] The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.

Tessellation

Moment (physics) Moment of force (often just moment) is the tendency of a force to twist or rotate an object; see the article torque for details. A moment is valued mathematically as the product of the force and the moment arm. The moment arm is the perpendicular distance from the point of rotation, to the line of action of the force. The moment may be thought of as a measure of the tendency of the force to cause rotation about an imaginary axis through a point.[1] (Note: In mechanical and civil engineering, "moment" and "torque" have different meanings, while in physics they are synonyms.

Neuroscience Neuroscience isthe scientific study of the nervous system.[1] Traditionally, neuroscience has been seen as a branch of biology. However, it is currently an interdisciplinary science that collaborates with other fields such as chemistry, computer science, engineering, linguistics, mathematics, medicine and allied disciplines, philosophy, physics, and psychology. The term neurobiology is usually used interchangeably with the term neuroscience, although the former refers specifically to the biology of the nervous system, whereas the latter refers to the entire science of the nervous system.The scope of neuroscience has broadened to include different approaches used to study the molecular, cellular, developmental, structural, functional, evolutionary, computational, and medical aspects of the nervous system. The techniques used by neuroscientists have also expanded enormously, from molecular and cellular studies of individual nerve cells to imaging of sensory and motor tasks in the brain. Recent theoretical advances in neuroscience have also been aided by the study of neural networks.

Neuroscience