To improve something is to make it better or bring it into a more desirable condition. Ameliorate shares this broad sense, but this formal verb is typically used to discuss circumstances that are more dire than what you might find with improve. For instance, you may hear of improving a workflow, or improving sound quality, but it is less likely that you'll hear ameliorate used in everyday contexts such as these. More commonly, you'll find ameliorate in discussion of oppressive, unjust, or difficult conditions, such as those brought by social or economic inequality or environmental degradation.

When a task or duty is so difficult to perform that doing so feels like a burden, it may be best described as onerous. Onerous comes from the Latin word for "burden," onus, which is used in English with the same meaning. A burden is something that is oppressively heavy, and indeed, when we use the word onerous, we evoke the idea of heaviness: an onerous undertaking is one so riddled or "heavy" with hardships it is difficult to bear. Onerous is also used to describe agreements, contracts, or guidelines that are so bogged down with legal obligations or restrictions, the intended benefits or advantages are outweighed.

There are many types of knowledge, and erudition is one of them. Erudition is a thorough, formal, and profound sort of knowledge obtained by extensive research. The term is often used to discuss knowledge in fields other than those of mathematics and the physical sciences—so you're more likely to encounter it in discussion of philosophy or literature than in discussion of biology. Erudition is not a high-frequency word in English, but when it is used, it's likely to be in a context of glowing appreciation, as something that inspires respect or awe.