The hyperlinks to biographical information in the poem's text are from the excellent source: J.J. O'Connor and E.F. Robertson, The MacTutor History of Mathematics Archive, University of St. Andrews, Scotland. Additional biographical and historical links are provided below for variety and pedagogical usefulness.
Jacob Bernoulli (1654-1705)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Bernoulli_Jacob.html
http://www.daviddarling.info/encyclopedia/B/Bernoulli.html
Jost Bürgi (1552-1632)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Burgi.html
Leonard Euler (1707-1783)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Euler.html
http://plus.maths.org/issue42/features/wilson/
Christian Goldbach (1690-1764)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Goldbach.html
Euler's correspondence with Goldbach: Lettre XV, November 25, 1731
http://math.dartmouth.edu/~euler/correspondence/letters/OO0729.pdf
Charles Hermite (1822-1901)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Hermite.html
Christiaan Huygens (1692-1695)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Huygens.html
Gottfried Leibniz (1646-1716)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Leibniz.html
http://www.gottfriedleibniz.com/
Nicolaus Mercator (1620-1687)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Mercator_Nicolaus.html
John Napier (1550-1617)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Napier.html
http://plus.maths.org/issue44/features/sangwin/index.html
http://www.johnnapier.com/
William Oughtred (1574-1660)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Oughtred.html
http://www.sliderulemuseum.com/REF/Oughtred_Aubrey.htm
Gregorius Saint-Vincent (1584-1667)
http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Saint-Vincent.html
Brook Taylor (1685-1731)
http://www-history.mcs.st-andrews.ac.uk/Biographies/Taylor.html
Wikipedia (http://en.wikipedia.org) is a rich online source of information about most of the topics mentioned in the poem. Unfortunately, Wikipedia's open-editing policy makes the accuracy of the information on its site uncertain. For this reason we provide links to different online sources. Whenever possible, we have chosen sites where the information is presented with students and educators in mind.
Bernoulli trials
http://www.cut-the-knot.org/Probability/BernoulliTrials.shtml
Calculus
http://math.mit.edu/~djk/calculus_beginners/chapter01/section02.html
Complex numbers
http://www.clarku.edu/~djoyce/complex/
Compound interest
http://plus.maths.org/issue11/features/compound/index.html
Continued fractions
http://www.maths.surrey.ac.uk/hostedsites/R.Knott/Fibonacci/cfINTRO.html#othercfs
http://archives.math.utk.edu/articles/atuyl/confrac/index.html
http://plus.maths.org/issue11/features/cfractions/
Derangements and the Hat-Check Problem
http://www.wmueller.com/precalculus/e/e6.html
http://notaboutapples.wordpress.com/2009/08/03/the-two-decks-of-cards-and-the-drunken-hat-check-girl/
Derivative
http://math.mit.edu/~djk/calculus_beginners/chapter04/section02.html
Differential Equations
http://khanexercises.appspot.com/video?v=-_POEWfygmU
http://www.math-atlas.org/ (click on Differential Equations)
e
http://ja0hxv.calico.jp/pai/ee1value.html (e to 200 billion digits)
http://www.mathpages.com/home/kmath400.htm (irrationality of e)
http://planetmath.org/encyclopedia/EIsTranscendental.html (transcendentality of e)
http://numbers.computation.free.fr/Constants/constants.html (online computation of e)
Euler's Identity
http://www.well.com/~davidu/euler.html
http://users.forthnet.gr/ath/kimon/Euler/Euler.htm
Exponential function
http://mathworld.wolfram.com/ExponentialFunction.html
i (imaginary unit)
http://www.clarku.edu/~djoyce/complex/numberi.html
Integral
http://math.mit.edu/~djk/calculus_beginners/chapter16/section01.html
Irrational numbers
http://www.cut-the-knot.org/do_you_know/numbers.shtml#rational
http://www.daviddarling.info/encyclopedia/I/irrational_number.html
Limit
http://www.coolmath.com/lesson-whats-a-limit-1.htm
Logarithm and natural logarithm (ln)
http://mathworld.wolfram.com/Logarithm.html
http://www.coolmath.com/algebra/17-exponentials-logarithms/09-special-logarithms-02.htm
http://demonstrations.wolfram.com/CalculatingIntegerLogarithmsInDifferentBases/
Number Theory
http://mathworld.wolfram.com/NumberTheory.html
http://www.math-atlas.org/ (click on Number Theory)
Pi (π)
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Pi_through_the_ages.html
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Pi_chronology.html
Probability
http://www.cut-the-knot.org/Probability/Dictionary.shtml
http://www.math-atlas.org/ (click on Probability and Statistics)
Rectangular hyperbola
http://mathworld.wolfram.com/RectangularHyperbola.html
Roots of unity
http://www.clarku.edu/~djoyce/complex/powers.html
Series (infinite sums)
http://plus.maths.org/issue19/features/infseries/
Slide rule
http://www.sliderule.ca/intro.htm
http://www.sliderulemuseum.com/?PHPSESSID=52598164a6abd4a522b5ef680a487335
http://demonstrations.wolfram.com/SlideRule/
Taylor series expansion
http://www.math.hmc.edu/calculus/tutorials/taylors_thm/
http://mathworld.wolfram.com/TaylorSeries.html
Transcendental numbers
http://www.daviddarling.info/encyclopedia/T/transcendental_number.html
http://www.cut-the-knot.org/do_you_know/numbers.shtml#algebraic