Here is a list of grammatical errors found in the text:
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Comma Placement: In "Problems that rapid urbanization in Southeast Asia can cause are, overcrowding, not enough houses, and pollution," the comma after "are" is incorrectly placed. It should be removed.
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Word Choice: In "With the big amount of people," the phrase "big amount" is awkward. It would be better as "large number" or "large amount" depending on the context, but as per your request, this should not be changed.
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Word Agreement: In "pollution will be more common since there will be much more people driving cars," "much more people" is grammatically incorrect. It should be "many more people" to agree with the countable noun "people."
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Redundancy/Clarity: The phrase "many people being homeless" could be seen as slightly unclear as "many people" implies a significant number, but it’s not a direct grammatical error.
These points summarize the grammatical errors without rephrasing.