Problems in Section 1 of GTM 167

Please post carefully solutions of the following ones:

1. Let be a field extension of . By defining scalar multiplication for and by , the multiplication in , show that is an vector space.

2. If is a field extention of , prove that iff .

What is GTM 167?

Chao cac ban,

Toi se khong noi lai vai tro cua ly thuyet truong va ly thuyet Galois. De hoc ly thuyet nay toi da chon cuon sach sau day

Field and Galois Theory (Graduate Texts in Mathematics) by Patrick Morandi

Trong khi doc cuon nay toi da gap phai van de la cac bai tap trong cuon nay kha kho, nhieu bai toi da co gang nhung giai khong ra, ma viec lam cac bai tap (cang nhieu cang tot) sau moi chuong la rat quan trong, no se giup toi nam vung ly thuyet hon.  Voi su dong tinh cua cac ban cua toi, toi quyet dinh lap box nay de chung ta cung nhau giai tat ca cac bai tap trong cuon sach do. Toi chac chan rang,  toi se hoc tot hon ly thuyet nay nho su giup do cua cac ban.  Xa hon nua, neu co the, chung toi se tap hop cac loi giai nay thanh mot file, no se la tai lieu huu ich cho cac ban hoc ly thuyet truong va ly thuyet Galois sau nay.

Ten cua box la GTM 167 vi cuon sach do nam trong chuoi Graduate Texts in Mathematics va no la cuon mang so 167.

Toi nghi rang box nay se co it nhat topic ,ung voi muc trong cuon sach do. Trong moi topic toi se post tat ca cac bai toan trong mot muc, sau do chung ta se cung nhau post loi giai cua cac bai toan do. Cac ban nen dung tieng Anh hoac tieng Viet khong dau khi post cac loi giai, va su dung trong cac post cua minh. Ve cach go cong thuc Toan cac ban co the vao trang About cua blog nay de xem qua, no thuc su rat don gian!

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Cam on cac ban.

Nguyen Trung Tuan.

Hay binh chon cho Ha Long thanh di san thien nhien the gioi

Minh chuan bi di bau cho Ha Long day, cac ban cung di bau luon di thoi. Hay vao cac link sau de biet them chi tiet:

1)http://vnexpress.net/Vietnam/Xa-hoi/Du-lich/2007/08/3B9F9AD5/

2)www.natural7wonders.com

Cach mo file *.djvu

Tai chuong trinh sau ve va cai no:

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Hoang hon

 

 Hoi sen teo.

Rieng mot goc troi, Ngo Thuy Mien

Hom truoc di hat karaoke voi bac Song Minh, bac the hien bai nay rat dat, theo em la hay hon chu ca si hat bai nay.

Cac ban quan tam co the download va nghe thu. 

Tac gia: Ngo Thuy Mien.

Tinh yeu nhu nang, nang dua em ve, ben dong suoi mo

… … …
Goi ten em mai, trong con me nay , minh nho thuong nhau.

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Two lemmas on linear sequences of order two

Note: My English is so bad but don’t worry about that!

A sequence is called linear of order two if there are real numbers such that

In this topic we’ll use ideas in proofs of two following lemmas to solve some Olympiad problems.

Cac bai Toan hinh hoc trong nam 2007

Cac bai Toan hinh hoc, dac biet la hinh hoc phang la mot phan khong the thieu trong cac de thi Toan QG cua cac nuoc va IMO. Trong topic nay chung ta se trao doi ve cac bai Toan hinh hoc da xuat hien trong cac de thi HSG QG cua cac nuoc va IMO trong nam 2007.

Co bao nhieu cach chung minh cho bat dang thuc a/(b+c)+b/(c+a)+c/(a+b)>=3/2?

Trong topic nay chung ta se xem bat dang thuc

co bao nhieu cach chung minh?