How is correct to say?

  1. According to my understanding
  2. According to my understandings

For instance how is correct to say

According to my understanding(s) the definition of derivative function (from mathematics) is as follows...

  • 1
    As a learner, I prefer none of them. However, I think adding some context would be very helpful – Cardinal Jul 15 '16 at 8:58
  • @Max I wonder if it is correct to say the plural "understandings" instead of the singular "understanding". – Pekov Jul 15 '16 at 9:21
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    In your example, we'd probably say, "As I understand it, ...." We tend to use "according to my understanding" to refer to situations and contexts rather than subjects and disciplines. "According to my understanding, the policy committee will meet to discuss this matter next week." "As I understand it, mixing vinegar and baking soda creates a chemical reaction that produces carbon dioxide gas." – Tᴚoɯɐuo Jul 15 '16 at 13:13
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    @Pekov - No, the plural "understandings" sounds very strange; use the singular understanding. Phenomena, like understanding, are usually referred to in the singular. – stangdon Jul 15 '16 at 13:41
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    In an informal sense you could use "According to my understandings..." in the sense that means "According to the things I know...". But it wouldn't seem literate at all. – user3169 Jul 15 '16 at 19:49

We are implying knowledge of a particular domain. More completely we might say

According to my understanding of calculus

while in principle we can use understandings as a plural, I've only ever seen it used in the sense of understanding meaning agreement between people.

However I would not use according to my understanding here. We use according to report the opinion of a third-party.

According to Delia Smith the best way to boil an egg is ...

Here we are stating our own understanding of the topic, and want to make it clear that we are open to correction, someone else may have a better understanding. So I would say

As I understand it, the definition ...

We rarely use according to me except in a somewhat jocular manner.

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    Google Books has over 60,000 instances of according to my understanding, so I can't endorse your implying that there's something inappropriate about the usage. – FumbleFingers Jul 15 '16 at 13:05
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    And 450,000 for "as I understand it" ;-) While there is no doubt that both expressions are used and understood I do think it's worth considering these subtle differences. I stand by the advice I give in my answer. – djna Jul 15 '16 at 13:12
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    I would have expected as I understand it to be more common. But given the numbers, I don't think this justifies implying that the less common form is "less than ideal" phrasing. It may also be worth noting that in my understanding has risen five-fold over recent decades (which I think weakens your "semantic" argument). – FumbleFingers Jul 15 '16 at 13:51

I understand what you mean by

According to my understanding

But I don't think it is commonly used. Especially since according is used for reporting. It also sounds like you are implying that you might be incorrect.

Some common expressions are

  1. as far as I know
    used for saying what you think is true when you think that there may be facts that you do not know, remember, etc.
  2. to my knowledge
    a. as I understand it
    b. as I know
  3. as I understand it; as I remember it
  4. The way I see it (usually used for opinions)
  5. If I understand correctly
  6. If I remember correctly; If memory serves me right

However, these expressions suggest that you might remember or understand something incorrectly.

If you are confident about your understanding or memory, then I don't think it is necessary to use an expression like "as far as I know". You would simply say

The definition of...

  • 2
    I think you're simply wrong when you say it's not commonly used. Per my comment to the same claim made in @djna's answer, it's a very common usage. – FumbleFingers Jul 15 '16 at 13:07

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