What This Document Is
This document, titled "100 Problems on Inequalities," is a collection of challenging mathematical problems focused on the topic of inequalities. It originates from coursework at MIT’s Mathematics for Computer Science (6.042J) course and was compiled by Amir Hossain Parvardi, with editorial contributions from Sayan Mukherjee. The problems are designed to test and expand understanding of inequality proofs and manipulations.
Why This Document Matters
This resource is valuable for students studying advanced mathematics, particularly those in computer science or related fields where rigorous proof techniques are essential. It’s suited for self-study, competition preparation (like math Olympiads), or as supplemental practice for a formal course on mathematical reasoning. The problems build skills in algebraic manipulation, logical deduction, and problem-solving within the context of inequalities.
Common Limitations or Challenges
This document presents *problems* only. It does not include detailed solutions, explanations of underlying concepts, or step-by-step guidance on how to approach inequality proofs. Users should have a solid foundation in algebraic techniques and proof strategies before attempting these problems. It is a practice resource, not a teaching tool.
What This Document Provides
The full document contains 100 distinct inequality problems, ranging in difficulty. The preview excerpt shows problems involving positive and non-negative real numbers, exploring relationships between sums, products, and roots. Specific problem types include proving inequalities involving multiple variables, finding maximum values under constraints, and establishing relationships between algebraic expressions. The problems cover a variety of inequality techniques and require creative application of mathematical principles. This preview shows problems 1-30, with a sampling of the types of inequalities included in the full set. The complete document does *not* include solutions.
