Suppose that: giả sử (rằng)

Giả sử sets up a situation to think through, like English "suppose" or "assuming". It opens the sentence, rằng (that) may follow, and the consequence comes after a comma or thì: Giả sử các yếu tố khác không đổi, …, assuming other factors stay the same, …

The difference from nếu (if) is the purpose. Nếu sets a condition that may well come true: Nếu mai mưa thì mình ở nhà. Giả sử asks the reader to accept something for the sake of argument, often something unlikely or only imagined, and then follows where it leads. That's why it's at home in papers, in maths and economics, and in reports that work through a scenario step by step.

People also use it when they think aloud: Giả sử anh trúng số thì anh làm gì? Suppose you won the lottery, what would you do? When the imagined thing is a worry, Saigon speech prefers lỡ (what if): Lỡ mai mưa thì sao?

Giả dụ is an older variant with the same meaning. It's rare now, so you only need to recognise it. For "assume" as a verb in a paper, writers use giả định: Mô hình giả định rằng …, the model assumes that …