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All Educational Materials for MAT 218A at University of California - Davis (UC-DAVIS)

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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 14: Linear Map, Surjective Function, Unit Circle

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1 May 2019
0
Enumerating the vertuces if a regular n-gon gives a homomorphism. 6 )) = (123456) hexagon on unit circle enumerated ccw starting with 1 at (1,0) 1 3 5,
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 4: Coset, Group Homomorphism, Permutation

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1 May 2019
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G, h nite groups gcd(|g|, |h|) = 1 ! : g h. Example (z15, +) (z4, +) order 15, 4 respectively. 115 (115) so ord (115|ord115 divisors of 15 is 1,3,5,15
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 12: Unit Circle, Dihedral Group

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1 May 2019
0
Let m matn n(r) then m on i it"s columns form an orthonormal collection. {ai} form an orthonormal collection of vectors in rn today studying o2 and so2
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture 15: MAT150A_DAY15_Oct31_Lecture

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1 May 2019
0
Then the following are equivalent: f is an isometry and f , f ( x ) f ( y ) = x y x , y rn. = a a = then a = b. 2 = 3 need to show f is linear. f ( x +
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 22: Conjugacy Class, American Broadcasting Company, Prime Number

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1 May 2019
0
120 = (e) + (ab) + (abc) + (abcd) + (abcde) + (ab)(cd) + (abc)(de) 60 = (e) + (abc) + (abcde) + (ab)(cd) obvi wrong bc 24 does not divide 60. Each one
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 8: Surjective Function, Group Homomorphism, Bijection

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1 May 2019
0
G nite group, h g a subgroup. (lagrange) |g| Denote [g : h] called the index of h in g. To show lagrange we built an equivalence relation x y xy 1 h. W
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 10: Normal Subgroup

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1 May 2019
0
G- group g1, g2 g st g1, g2 have nite order but g1g2 has in nite order. If g1g2 = g2g1 then g1g2 has nite order provided both g1, g2 have. Homework: sh
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 17: Platonic Solid, Cyclic Group, Axa

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1 May 2019
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 11: Coset, Normal Subgroup, Surjective Function

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1 May 2019
0
Let h g be a subgroup, then h is normal a g, ah = ha. H =< (12) >= {e, (12)} eh = h (12)h = {(12), e} (13)h = {(13), (123)} (23)h = {(23), (132)} (123)
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 28: Bijection, Identity Function, Permutation Matrix

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1 May 2019
0
Announcements: oh next week only, oct 1-5, mwf 4-5. Recall: elements of sn are bijective functions p = {1, , n} {1, , n, product in sn corresponds to c
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