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Advanced Scientific Mathematics

 

stemNRICH : Science, Technology, Engineering, Mathematics enriched
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Advanced Scientific Mathematics
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Advanced Scientific Mathematics
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Advanced Scientific Mathematics

 

 

Welcome to the Advanced Scientific Mathematics section of stemNRICH . This contains a set of activities designed to develop the advanced applied mathematical skills needed to make the most of the study of the physical sciences or engineering at university. These problems naturally follow on from the more elementary core scientific mathematics section of stemNRICH and are primarily intended for those who intend to study physics, engineering or applied mathematics at university.

 

 

 

Area of maths Style Question Description
Rates of change
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Advanced Scientific Mathematics
Maths Filler 2 Practise looking at rates of change as this vessel fills with water.
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Advanced Scientific Mathematics
Immersion Various solids are lowered into a beaker of water. How does the water level rise in each case?
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Advanced Scientific Mathematics
Brimful Rotate the curves to make some mathematical vessels.
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Advanced Scientific Mathematics
Brimful 2 Which of these mathematical flasks will eventually fill up with water?
Curves
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Advanced Scientific Mathematics
Curve Fitter Use your skill to try to fit a cubic equation through these three points.
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Advanced Scientific Mathematics
Curve Fitter 2 Can you make a cubic which has a certain distance between the turning points?
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Advanced Scientific Mathematics
Implicitly Can you find the shape of this implicity defined function?
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Advanced Scientific Mathematics
Whose line graph is it anyway? Which line graphs, processes and equations go together?
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Advanced Scientific Mathematics
Can you sketch these difficult curves, which have uses in mathematical modelling?
Calculus Calculus is involved in many problems on stemNRICH. See the physNRICH and engNRICH pages for various particular examples.
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Advanced Scientific Mathematics
Can you hit the target functions using a set of input function and a little calculus and algebra?
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Advanced Scientific Mathematics
Integration Matcher Which curves, integrals and differentials go together?
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Advanced Scientific Mathematics
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Differential equations You will also find lots of differential equations problems in various sections on the physNRICH and engNRICH pages
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Advanced Scientific Mathematics
Differential Equation Matcher Match the descriptions of physical processes to these differential equations.
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Advanced Scientific Mathematics
Explore the possible mathematical solutions to the non-linear order of reaction equation from chemistry.
Series and expansions
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Advanced Scientific Mathematics
Production Equation Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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Advanced Scientific Mathematics
Stirling Work See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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Advanced Scientific Mathematics
What Do Functions Do for Tiny x? How do these familiar functions behave for very small values?
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Advanced Scientific Mathematics
Get further into power series using the fascinating Bessel's equation.
Powers, roots and logarithms See also the Logarithms and pH problems on the chemNRICH pages
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Advanced Scientific Mathematics
Power Match Can you locate these values on this interactive logarithmic scale?
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Advanced Scientific Mathematics
Debt Race Who will be the first investor to pay off their debt?
Probability and distributions
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Advanced Scientific Mathematics
pdf Matcher What scientific stories can you match to these pdf curves?
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Advanced Scientific Mathematics
Circle PDF How can an arc of a circle be a pdf?
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Advanced Scientific Mathematics
Scale Invariance By exploring the concept of scale invariance, find the probability that a random piece of real-world data begins with a 1.
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Advanced Scientific Mathematics
Into the Exponential Distribution Get into the exponential distribution through an exploration of its pdf.
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Advanced Scientific Mathematics
Into the Normal Distribution Get into the normal distribution through an exploration of its pdf.
Statistics
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Advanced Scientific Mathematics
Stats Statements This question gives you 10 statistical statements. Develop your statistical intuition by asking yourself are they sometimes, always, nearly always, almost never or never true?'
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Advanced Scientific Mathematics
Overbooking Why do airlines overbook?
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Advanced Scientific Mathematics
The Wrong Stats Why MUST these statistical statements be at least a little bit wrong?
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Advanced Scientific Mathematics
Aim High How much wheat should this farmer plant to minimise his expected loss?
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Advanced Scientific Mathematics
Time to Evolve 2 How would you model the time between your birth and that of your grandfather?
Trigonometry
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Advanced Scientific Mathematics
Flight Path Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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Advanced Scientific Mathematics
Loch Ness Draw graphs of the sine and modulus functions and explain the humps.
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Advanced Scientific Mathematics
Spherical Triangles on Very Big Spheres Find out about spherical triangles and decide if telecoms engineers need to know about such things.
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Advanced Scientific Mathematics
Taking Trigonometry Seriesly Look at the advanced way of viewing sin and cos through their power series.
Complex numbers
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Advanced Scientific Mathematics
A nice introduction to complex numbers, including many exercises for the reader.
  More on the way More on the way
Vectors
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Advanced Scientific Mathematics
Spotting the Loophole A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
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Advanced Scientific Mathematics
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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Advanced Scientific Mathematics
Follow Ulaf, Vicky and Wilber on a vector walk to determine the locations nearest to the origin.
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Advanced Scientific Mathematics
Air Routes An application of vectors and scalar products in a very practical setting.
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Advanced Scientific Mathematics
Explore the meaning of the scalar and vector products and see how the two are related
Vectors and matrices
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Advanced Scientific Mathematics
What quadrilaterals can you transform this pair of squares into?
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Advanced Scientific Mathematics
Explore the mathematics of matrix transformations with these 10 individual questions.
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Advanced Scientific Mathematics
Explore the algebraic and geometric properties of matrices with these 5 individual questions.
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Advanced Scientific Mathematics
Crystal Symmetry Use vectors and matrices to explore the symmetry properties of Caesium Chloride.
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Advanced Scientific Mathematics
Explore how matrices can fix vectors and vector directions.?
Can you make matrices which will fix one lucky vector and crush another to zero?
Numerical methods
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Advanced Scientific Mathematics
Root Hunter In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
     
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Advanced Scientific Mathematics
Building Approximations for Sin(x) Build up the concept of the Taylor series.
Decision making and algorithms
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Advanced Scientific Mathematics
Testing Strategy Investigate ways in which you could implement a scoring system for a multiple choice test.
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