First of all, i would like to appologise if there is already a topic related to this on which i could have posted. I was not able to find it but also only skimmed through the search results.

Mathematics has not been one of strong points. In middle school i struggled with it - i didn't spend any time at it. In highschool i was forced into it because i needed it to further my studies and go to University later on. However i memorised it. It was for the most part without understanding, and while it got me into university i did not grasp it. Somehow, though, because i did so much of it i started to become curious; i slowly became more interested in it for, well just the concepts it brings. The problem is that i have many loopholes and gaps in my knowledge of it. Some parts i grasp, some i don't.

As a result i have decided to go back and fill in those gaps. The best way i could think of doing this was just to revisit the topics covered from middle school up until university, and eventually beyond. For this ofcourse i picked out some textbooks and decided upon a general plan. Knowing that in the US the topics are covered roughly in this order: Algebra I, Geometry, Algebra II with Trigonometry, Pre-calculus, Calculus (up until University), that is the order in which i think it is best to tackle them. My plan is to go through the respective textbooks and if i find an area i already understand then i will fast forward through it, but hopefully that will also allow me to focus on the parts which i dont grasp - the gaps i mentioned.

Here are the textbooks i've decided upon after some browsing on the internet:

Algebra I: Expressions, Equations and Applications, by Foerster

Geometry, by Jacobs

Algebra and Trigonometry: Functions and Applications, Foerster

This should bring me up to speed with Pre-calculus level (which i also understand is similar to Algebra II and Trigonometry, except that it might bring some additional depth and also introduce limits). The dilemma i face is which Pre-calculus textbook to choose? The only one i have considered so far is Larson's Precalculus with Limits, 2nd Edition, but i was wondering if anyone might suggest better ones? I've seen 'Principles of Mathematics' , by Allendoerfer mentioned a few times and read very pleasant commentaries on it. Would this cover the same subject matter or beyond it?

Going past the pre-calculus level, i was thinking of one of these for the Calculus.

https://www.amazon.com/dp/0321587995/?tag=pfamazon01-20

OR

https://www.amazon.com/dp/0471698040/?tag=pfamazon01-20

Would you have other recommandations on this or on picking one of the two in particular? Also, while we're at the Calculus matter i would like to ask: Would a whole Calculus textbook cover Calculus I, II and III aswell, and perhaps even go beyond?

Suggestions and recommendations in this would be very welcome.

Assuming i go beyond the Calculus topics (when and if), what subject matter should i next pursue? What would follow next in the educational pattern? This is an area i am particularly blurry about since i didn't go beyond Calculus when i entered University, so i don't really have any idea what lies beyond. Suggestions, recommendations and such would be most welcome in this area. I would like to outline that i am not interested in one area that would be particularly useful to this career or that career, rather i am looking to broaden my knowledge on mathematics with this.

I've seen this mentioned quite a few times and (even to someone as unknowing as me) it should be very interesting. What textbooks or material would you recommend for this? Perhaps something at an introductory level at first (as i am totally new to this field), and then further recommendations to build up upon it and perhaps reach more advanced levels.

I would like to emphasise the fact that i'm interested in learning and understanding the mathmatical concepts involved, not just to say i've done them. I've also read a little bit and will continue to read the 'who wants to be a mathematician' sticky in this forum and it seems very interesting, especially since it contains some unique reading and information.

That would be it. I guess what i'm asking for is some indications about how i should tackle the task at hand, preferably with suggestions of materials (textbooks) on the mentioned topics.

Thank you for reading :)

Mathematics has not been one of strong points. In middle school i struggled with it - i didn't spend any time at it. In highschool i was forced into it because i needed it to further my studies and go to University later on. However i memorised it. It was for the most part without understanding, and while it got me into university i did not grasp it. Somehow, though, because i did so much of it i started to become curious; i slowly became more interested in it for, well just the concepts it brings. The problem is that i have many loopholes and gaps in my knowledge of it. Some parts i grasp, some i don't.

As a result i have decided to go back and fill in those gaps. The best way i could think of doing this was just to revisit the topics covered from middle school up until university, and eventually beyond. For this ofcourse i picked out some textbooks and decided upon a general plan. Knowing that in the US the topics are covered roughly in this order: Algebra I, Geometry, Algebra II with Trigonometry, Pre-calculus, Calculus (up until University), that is the order in which i think it is best to tackle them. My plan is to go through the respective textbooks and if i find an area i already understand then i will fast forward through it, but hopefully that will also allow me to focus on the parts which i dont grasp - the gaps i mentioned.

Here are the textbooks i've decided upon after some browsing on the internet:

Algebra I: Expressions, Equations and Applications, by Foerster

Geometry, by Jacobs

Algebra and Trigonometry: Functions and Applications, Foerster

This should bring me up to speed with Pre-calculus level (which i also understand is similar to Algebra II and Trigonometry, except that it might bring some additional depth and also introduce limits). The dilemma i face is which Pre-calculus textbook to choose? The only one i have considered so far is Larson's Precalculus with Limits, 2nd Edition, but i was wondering if anyone might suggest better ones? I've seen 'Principles of Mathematics' , by Allendoerfer mentioned a few times and read very pleasant commentaries on it. Would this cover the same subject matter or beyond it?

**Calculus**Going past the pre-calculus level, i was thinking of one of these for the Calculus.

https://www.amazon.com/dp/0321587995/?tag=pfamazon01-20

OR

https://www.amazon.com/dp/0471698040/?tag=pfamazon01-20

Would you have other recommandations on this or on picking one of the two in particular? Also, while we're at the Calculus matter i would like to ask: Would a whole Calculus textbook cover Calculus I, II and III aswell, and perhaps even go beyond?

Suggestions and recommendations in this would be very welcome.

**Going Beyond Calculus**Assuming i go beyond the Calculus topics (when and if), what subject matter should i next pursue? What would follow next in the educational pattern? This is an area i am particularly blurry about since i didn't go beyond Calculus when i entered University, so i don't really have any idea what lies beyond. Suggestions, recommendations and such would be most welcome in this area. I would like to outline that i am not interested in one area that would be particularly useful to this career or that career, rather i am looking to broaden my knowledge on mathematics with this.

**Mathematical reasoning and logic**I've seen this mentioned quite a few times and (even to someone as unknowing as me) it should be very interesting. What textbooks or material would you recommend for this? Perhaps something at an introductory level at first (as i am totally new to this field), and then further recommendations to build up upon it and perhaps reach more advanced levels.

I would like to emphasise the fact that i'm interested in learning and understanding the mathmatical concepts involved, not just to say i've done them. I've also read a little bit and will continue to read the 'who wants to be a mathematician' sticky in this forum and it seems very interesting, especially since it contains some unique reading and information.

That would be it. I guess what i'm asking for is some indications about how i should tackle the task at hand, preferably with suggestions of materials (textbooks) on the mentioned topics.

Thank you for reading :)

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