Karl Heinz Dovermann,   Professor

Research Papers

Calculus Lecture Notes for Math 161

Office	Phone	Email
Keller Hall 405	(808) 956-4654	heiner@math.hawaii.edu
Spring 2026
Course title	Course number	Room	Hours
Intro. Advanced Mathematics	Math 321	Keller 403	MWF 11:30--12:20
Number Theory	Math 420	Keller 314	MWF 1:30--2:20
3 Manifolds	Math 649	Keller 313	TR 9:00--10:15
Office hours	MTWRF 12:30 -- 1:20, or by appointment

Announcement for Math 321 (Spring 2026):

• HW1, due 1/14, Problems 1.1.1 and 1.1.3 in Section 1.1.7.
• HW2, due 1/16, Problems 1.2.1, 1.2.6, and 1.2.9 in Section 1.2.7.
• HW3, due 1/21, Consider a regular pentagon with side length A and diagonal length D. Construct a smaller pentagon inside of it, as done in class. What is its diagonal length?
• HW4, due 1/23, Problems 2.1.3, 2.1.4, and 2.1.11 in Section 2.1.7.
• HW5, due 1/26, Problems 2.2.2, 2.2.4, and 2.2.6 in Section 2.2.6. Lines in general position (no two are parallel, and no three intersect in one point) partition the plane into how many regions. Find a formula, and prove it.
• HW 6, due 1/28: Show 1x3 + 2x4 + 3x5 + ... + n x (n+2) = n(n+1)(2n+7)/6, and 1 + 3 + 5 + ... + (2n-1) = n^2. Show, for n > 27 we have non-negative integers x and y, so that n = 5x + 8y.
• HW7, due 1/30, Problems 2.2.9 and 2.2.18 on page 45f.
• HW8, due 2/2, Problems 2.3.2, 2.3.5, 2.3.7, 2.3.10 on page 53f.
• HW9, due 2/4.
• HW10, due 2/6, Problems 2.4.2, 2.4.3, 2.4.4, 2.4.7 on page 59.
• Catch up with revisions.
• HW11, due 2/13, Prove, or disprove, that the composition of two equivalence relations is an equivalence relation.
• HW12 Bring question for review session.
• HW13, due 2/27, For a function f show that the following are equivalent: (1) f is injective, (2) f has a left inverse, and (3) f satisfies left cancellation.
• HW14, due 3/2, Problem 3.4.7 on page 86. Make a composition table for the symmetries of an equilateral triangle, motions sending the triangle back to itself.
• HW15, due 3/4, Problem 5.2.4, 5.2.5, 5.2.7 on page 132.
• HW16, due 3/9, Find a bijective funtion h_: A_ -. B+. For details, use your class notes.
• Syllabus for Math 321
• First exam (Spring 26)
• Final exam (Fall 23).
• Second exam (Fall 23).
• First exam (Fall 23).
• First exam (Summer 22).
• First exam (Summer 20).
• Second exam (Summer 20).
• Final exam (Summer 20).
• First exam (Spring 19).
• First exam (Summer 16) with solutions
• Second exam (Summer 16) with solutions
• Relations
• First exam (Summer 15) with solutions
• Second exam (Summer 15) without solutions
• 1st 321 exam Spring 2008
• 1st 321 exam Spring 2010
• 1st 321 exam Fall 2012
• 1st 321 exam Summer 2013
• 1st 321 exam Spring 2014
• 2nd 321 exam Spring 2010
• 2nd 321 exam Fall 2012
• 321 final Spring 2008
• 321 final Spring 2012
• 321 final Fall 2012
• 321 final Fall 2014
• 321 final Summer 2016
• 321 final Summer 2017

Announcement for Math 420 (Spring 2026):

• Prof. Guerzhoy's Math 420 syllabus
• Syllabus for Math 420
• HW1, due 1/14: p.7 #7, 10 and p.10 #4
• HW2, due 1/16: p.14 #5, and p.21f #2, 4
• HW3, due 1/23: p.34 #3, 6, and p.38 #2, 5
• HW4, due 1/26: p.40 #1, 2
• HW5, due 1/28: p.44 #4
• HW6, due 1/30: p.52 #6, and p. 61 #2, 3
• HW7, due 2/2: p.61 #1
• HW8, due 2/4: p.63 #2, 6, 9, 10.
• HW9, due 2/6: p.71 #6.
• HW10, due 2/11: p.74 #7, 8.
• HW11, due 2/13 : p.82 #11, 13, 14, 15.
• HW12, due 2/18 Exam quaestions.
• HW13, due 3/2: p.97 #6,7.
• HW14, due 3/4: p.99 #15, 16.
• HW15, due 3/9: p.124 #4, 6.

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