Using “would” with the present tense in conditional clauses

I have met such sentence in my tutorial text:

"Today my brother has announced that he is going to enter the university next year. I wondered if he had thought it over properly. He would be able to pass all the exams providing he studies at full speed, wouldn't he?"

I wonder if we can use "would" with present tense in the conditional clause. I feel that it may have something with subjunctive uncertainty, but I'm not sure. All grammar rules I've found prescribe to use "will" instead of "would" in this example, as it is 1st conditional. Can you tell me, please, if such usage is ok and how can it be explained grammatically?

Another example I've met on this forum while trying to browse the answer to my question (It was a part of the answer to a related question, but it didn't clarify the usage rules):

"If you are a mathematician, and understand the conjugal relationship between real and imaginary numbers, you would see that the subjunctive is the imaginary conjugate of the real world.