What is General math: Definition and 20 Discussions

Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and analysis. Nearly all countries throughout the world, except the United States, follow this type of curriculum.In the United States, topics are usually integrated throughout elementary school up to the eighth grade. Beginning with high school level courses, topics are usually separated so that one year a student focuses entirely on algebra, the next year entirely on geometry, and then another year of algebra and later an optional fifth year of analysis (calculus). The one exception in the American high school curriculum is the fourth year of math, typically referred to as precalculus, which usually integrates algebra, analysis, trigonometry, and geometry topics. Statistics may be integrated into all the courses or presented as a separate course.
New York State began using integrated math curricula in the 1980s, but recently returned to a traditional curriculum. A few other localities in the United States have also tried such integrated curricula, including Georgia, which mandated them in 2008 but subsequently made them optional. More recently, a few other states have mandated that all districts change to integrated curricula, including North Carolina, West Virginia and Utah. Some districts in other states, including California, have either switched or are considering switching to an integrated curriculum.Under the Common Core Standards adopted by most states in 2012, high school mathematics may be taught using either a traditional American approach or an integrated curriculum. The only difference would be the order in which the topics are taught. Supporters of using integrated curricula in the United States believe that students will be able to see the connections between algebra and geometry better in an integrated curriculum.
General mathematics is another term for a mathematics course organized around different branches of mathematics, with topics arranged according to the main objective of the course.
When applied to primary education, the term general mathematics may encompass mathematical concepts more complex than basic arithmetic, like number notation, addition and multiplication tables, fractions and related operations, measurement units.
When used in context of higher education, the term may encompass mathematical terminology and concepts, finding and applying appropriate techniques to solve routine problems, interpreting and representing practical information given in various forms, interpreting and using mathematical models, and constructing mathematical arguments to solve familiar and unfamiliar problems.

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  1. jedishrfu

    B Maze Proof and Statistical Mechanics

  2. LCSphysicist

    I Page 183-184 of Howard George's group book

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  3. M

    I Eccentric anomaly of ellipse-circle intersections

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  4. mcastillo356

    B Cosecant function: notation for the domain and range -- Am I right?

    Hi, PF There are two ways to write domain and range of a function: through set notation, or showing intervals. I've chosen the set notation, and, for ##y=\csc x##, this is the attempt: $$\text{D}:\{x\,|\,x\not\in{n\pi},\,n\not\in{\mathbb{Z}}\}$$ $$\text{R}:\{f(x)\,|\,x=\mathbb{R}\(-1,1)\}$$...
  5. DaveC426913

    B Simple Combo/Permute calculation

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  6. M

    Identifying the type of expression

    TL;DR Summary: ##(1+ \frac1x)^2 - (1-\frac1x)^2## ##(z+2)^2 -5(z+2)## Upon simplifying the first I get ##\frac4x##. So isn’t the first expression fractional? Upon simplifying the second I get a Quadratic expression.
  7. ValenceElectron

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  8. A

    I The Ratio of Total Derivatives

    If we have two functions C(y(t), r(t)) and I(y(t), r(t)) can we write $$\frac{\frac{dC}{dt}}{\frac{dI}{dt}}=\frac{dC}{dI}$$?
  9. Cantor080

    Other Utility of a general math book introducing subjects not in historical order?

    I have Abstract Algebra Course, and my teacher is using the book, "Abstract Algebra" of David S. Dummit, and Richard M.Foote. This book, and other books which my teachers are using for the courses, seem to give definitions, theorems, and problems, in no historical order or are not mentioning the...
  10. Mario

    Circles and Euler spiral (repost from general math)

    Hi, i have this problem..., giving two circle (example radius 1 = 500 units, radius 2 = 200 units, distance between centers = 275.73 units) find Euler Spiral (aka Cornu spiral, aka Clothoid https://en.wikipedia.org/wiki/Euler_spiral) tangent giving circle (unknown tangent points). For this...
  11. 1

    I Convert 2 variables into 1 representative variable

    I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B: Below is an example with C=A+B, which makes Set 2 the highest value: Set 1: A=65, B=75, C=140; Set 2: A=50, B=100, C=150; Set 3: A=54, B=90, C=144; Set 4: A=72, B=72, C=144; Set 5: A=71, B=73...
  12. F

    I Two questions about general math

    Is it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ? And I have another doubt. Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous...
  13. PsychonautQQ

    Calculus / general math related question

    Let f and g be twice differentiable real-valued functions. If f'(x) > g'(x) for all values of x, which of the following statements must be true? A) f(x) > g(x) B) f''(x) > g''(x) C) f(x) - f(0) > g(x) - g(0) D) f'(x) - f'(0) > g'(x) - g'(0) E) f''(x) - f''(0) > g''(x) - g''(0) The correct...
  14. T

    Calculating Weighted Averages in a Course

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  15. P

    General math formatting question (simple)

    Homework Statement Homework Equations The Attempt at a SolutionHi, so this is just a general question about how math homework should be submitted. I seem to change between formats, and I'd like to finally get an answer on how I should be doing things.Say I'm working on a problem with a formula...
  16. dkotschessaa

    Exploring Math Through Books: A Look at General Works on Mathematics

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  17. T

    A general math theory on the quantum harmonic oscillator?

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  18. M

    Good book for me to review general math

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  19. S

    Which Books Are Recommended for Learning General Math?

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