Pronunciations

For myself and my non-native-English-speaker friends

Pronunciation (approximate, but note the accent)

determine     -- dəTErmən   [Listen]     (not "determayn")
infinite           --   INfənət   [Listen]        (not "infaynayt")  
                          [but  finite  -- faynayt]
relative          --  RElədiv   [Listen]        (not "releytiv")
derivative      -- deRIvah-tiv                   (not "deriveytiv")
differentiable -- difəRENSHəbəl  [Listen]   

Names

Cauchy -- Koh-SHEE
Einstein -- AYN -shtayn  
Huygens  -- HOY-hens
Banach  -- BAnah           (not "banak")  
Poincare  -- puan-ka-REH
Schroedinger  -- close to shredingher   (not shrodinjer)
Viette -- vyet

Grammar

Between you and me  (Not: "Between you and I")
Whom did you see  (Not "Who did you see")

Ether:   "Let's see what it looks like"
or:        "Let's see how it look" 

but NOT:     "Let's see how it looks like"