Important Olympiad-inequalities
$begingroup$
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality soft-question contest-math big-list
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
$endgroup$
add a comment |
$begingroup$
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality soft-question contest-math big-list
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
$endgroup$
add a comment |
$begingroup$
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality soft-question contest-math big-list
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
$endgroup$
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality soft-question contest-math big-list
inequality soft-question contest-math big-list
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
asked 5 hours ago
Dr. MathvaDr. Mathva
1,190317
1,190317
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered 5 hours ago
OldboyOldboy
8,1351935
$endgroup$
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
16 Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered 5 hours ago
OldboyOldboy
8,1351935
$endgroup$
add a comment |
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered 5 hours ago
OldboyOldboy
8,1351935
$endgroup$
add a comment |
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered 5 hours ago
OldboyOldboy
8,1351935
$endgroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered 5 hours ago
OldboyOldboy
8,1351935
edited 4 hours ago
answered 5 hours ago
OldboyOldboy
8,1351935
answered 5 hours ago
OldboyOldboy
8,1351935
answered 5 hours ago
OldboyOldboy
8,1351935
8,1351935
add a comment |
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
16 Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
$endgroup$
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
16 Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
$endgroup$
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
16 Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
$endgroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
16 Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
answered 4 hours ago
Michael RozenbergMichael Rozenberg
103k1891195
103k1891195
add a comment |
add a comment |
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