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Improve mathematical writing skills for 1st-year undergraduates through 1.5 hours per week over 2 semesters. Topics include vector methods and distances between lines.
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Writing Enhancement for Mathematics Undergraduates 1st year undergraduates 1½ hours per week 2 semesters, 10 hours per semester
Writing Enhancement for Mathematics Undergraduates Further Vector Methods - Distance Between Two Lines A pair of two lines satisfy one of three conditions 1. They are parallel 2. The two lines intersect at a point 3. They are skew lines i.e. they are not parallel and they never meet. The shortest distance between two skew lines will lie along an imaginary line which is perpendicular to both the two original lines. This imaginary line joins the points on the two lines which are closest to each other. In the diagram below, the lines are drawn as long, thin triangles to emphasize the three-dimensional nature e.g. the lines tapering away into the distance. There is NO crossing point in the right-part of the diagram.
Writing Enhancement for Mathematics Undergraduates The two lines are (without loss of generality, r1 = a + b and r2 = c + μd. An algorithm for finding the two closest points and the distance between them is as follows. Step 1 :- Find n = b × d i.e. a vector perpendicular to both lines Step 2 :- Let r2 = r1 + kn i.e. c + μd = a + b + kn i.e. a vector from one line to the other is perpendicular to both lines Step 3 :- From the results of step 2, form three equations in , μ and k. (i.e. one equation from each of the x, y, and z-components) Step 4 :- Solve the equations in step 3 to find , μ and k Step 5 :- a + b and c + d are the closest points on the two lines Step 6 :- Find the distance between the two points
Writing Enhancement for Mathematics Undergraduates A king wants his daughter to marry the smartest of three extremely intelligent young princes, and so the king's wise men have devised an intelligence test. The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and a hat is placed on each of their heads, while the remaining hats are hidden in a different room.
Writing Enhancement for Mathematics Undergraduates The king tells them that the first prince to deduce the colour of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed. You are one of the princes. You see 2 white hats on the other prince's heads. After some time you realize that the other prince's are unable to deduce the colour of their hat, or are unwilling to guess. What colour is your hat? Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the king is a man of his word, and he has said that the test is a fair test of intelligence and bravery.
Writing Enhancement for Mathematics Undergraduates If your hat was black, then the other two princes would each see one white hat and one black hat. This would not be fair as they would not be starting with the same initial information as you and they would only have a fifty per cent chance of guessing the colour of their hat. Therefore, if the king is playing fair, which he must be since he said the test was fair, your hat must be white since each prince must be looking at two white hats.
Writing Enhancement for Mathematics Undergraduates English tutor from the University Language Centre Graduate Teaching Assistant from the Maths Dept
Writing Enhancement for Mathematics Undergraduates problems time – Wednesday afternoon content – difficult to select
